Relevant bibliographies by topics / Group homomorphism

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Group homomorphism'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Group homomorphism"

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DAY, MATTHEW B. "EXTENSIONS OF JOHNSON'S AND MORITA'S HOMOMORPHISMS THAT MAP TO FINITELY GENERATED ABELIAN GROUPS." Journal of Topology and Analysis 05, no. 01 (March 2013): 57–85. http://dx.doi.org/10.1142/s1793525313500027.

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We extend each higher Johnson homomorphism to a crossed homomorphism from the automorphism group of a finite-rank free group to a finite-rank abelian group. We also extend each Morita homomorphism to a crossed homomorphism from the mapping class group of once-bounded surface to a finite-rank abelian group. This improves on the author's previous results [5]. To prove the first result, we express the higher Johnson homomorphisms as coboundary maps in group cohomology. Our methods involve the topology of nilpotent homogeneous spaces and lattices in nilpotent Lie algebras. In particular, we develop a notion of the "polynomial straightening" of a singular homology chain in a nilpotent homogeneous space.
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Kepert, Andrew G. "The Range of Group Algebra Homomorphisms." Canadian Mathematical Bulletin 40, no. 2 (June 1, 1997): 183–92. http://dx.doi.org/10.4153/cmb-1997-022-6.

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AbstractA characterisation of the range of a homomorphism between two commutative group algebras is presented which implies, among other things, that this range is closed. The work relies mainly on the characterisation of such homomorphisms achieved by P. J. Cohen.
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CABRER, LEONARDO, and DANIELE MUNDICI. "RATIONAL POLYHEDRA AND PROJECTIVE LATTICE-ORDERED ABELIAN GROUPS WITH ORDER UNIT." Communications in Contemporary Mathematics 14, no. 03 (June 2012): 1250017. http://dx.doi.org/10.1142/s0219199712500174.

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An ℓ-groupG is an abelian group equipped with a translation invariant lattice-order. Baker and Beynon proved that G is finitely generated projective if and only if it is finitely presented. A unital ℓ-group is an ℓ-group G with a distinguished order unit, i.e. an element 0 ≤ u ∈ G whose positive integer multiples eventually dominate every element of G. Unital ℓ-homomorphisms between unital ℓ-groups are group homomorphisms that also preserve the order unit and the lattice structure. A unital ℓ-group (G, u) is projective if whenever ψ : (A, a) → (B, b) is a surjective unital ℓ-homomorphism and ϕ : (G, u) → (B, b) is a unital ℓ-homomorphism, there is a unital ℓ-homomorphism θ : (G, u) → (A, a) such that ϕ = ψ ◦ θ. While every finitely generated projective unital ℓ-group is finitely presented, the converse does not hold in general. Classical algebraic topology (à la Whitehead) is combined in this paper with the Włodarczyk–Morelli solution of the weak Oda conjecture for toric varieties, to describe finitely generated projective unital ℓ-groups.
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MORDESON, J. N., and P. S. NAIR. "FUZZY MEALY MACHINES: HOMOMORPHISMS, ADMISSIBLE RELATIONS AND MINIMAL MACHINES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 04, no. 01 (February 1996): 27–43. http://dx.doi.org/10.1142/s0218488596000032.

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Homomorphisms and admissible relations of fuzzy Mealy machines are studied. Admissible relations play a role similar to normal subgroups in group theory. The kernel of a homomorphism is shown to be an admissible relation. Conversely, corresponding to an admissible relation, there exists a homomorphism. The fundamental theorem on homomorphisms; and the existence and uniqueness of minimal machines are also presented.
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Reyes, Edgar N. "Homomorphisms of ergodic group actions and conjugacy of skew product actions." International Journal of Mathematics and Mathematical Sciences 19, no. 4 (1996): 781–88. http://dx.doi.org/10.1155/s0161171296001081.

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LetGbe a locally compact group acting ergodically onX. We discuss relationships between homomorphisms on the measured groupoidX×G, conjugacy of skew product extensions, and similarity of measured groupoids. To do this, we describe the structure of homomorphisms onX×Gwhose restriction to an extension given by a skew product action is the trivial homomorphism.
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BRZDȨK, JANUSZ. "CONTINUITY OF MEASURABLE HOMOMORPHISMS." Bulletin of the Australian Mathematical Society 78, no. 1 (August 2008): 171–76. http://dx.doi.org/10.1017/s0004972708000610.

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AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.
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Selvachandran, Ganeshsree, and Abdul Razak Salleh. "On Normalistic Vague Soft Groups and Normalistic Vague Soft Group Homomorphism." Advances in Fuzzy Systems 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/592813.

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We further develop the theory of vague soft groups by establishing the concept of normalistic vague soft groups and normalistic vague soft group homomorphism as a continuation to the notion of vague soft groups and vague soft homomorphism. The properties and structural characteristics of these concepts as well as the structures that are preserved under the normalistic vague soft group homomorphism are studied and discussed.
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Hirshon, Ron, and David Meier. "Groups with a quotient that contains the original group as a direct factor." Bulletin of the Australian Mathematical Society 45, no. 3 (June 1992): 513–20. http://dx.doi.org/10.1017/s0004972700030422.

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We prove that given a finitely generated group G with a homomorphism of G onto G × H, H non-trivial, or a finitely generated group G with a homomorphism of G onto G × G, we can always find normal subgroups N ≠ G such that G/N ≅ G/N × H or G/N ≅ G/N × G/N respectively. We also show that given a finitely presented non-Hopfian group U and a homomorphism φ of U onto U, which is not an isomorphism, we can always find a finitely presented group H ⊇ U and a finitely generated free group F such that φ induces a homomorphism of U * F onto (U * F) × H. Together with the results above this allows the construction of many examples of finitely generated groups G with G ≅ G × H where H is finitely presented. A finitely presented group G with a homomorphism of G onto G × G was first constructed by Baumslag and Miller. We use a slight generalisation of their method to obtain more examples of such groups.
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CHILDERS, LEAH R. "SIMPLY INTERSECTING PAIR MAPS IN THE MAPPING CLASS GROUP." Journal of Knot Theory and Its Ramifications 21, no. 11 (August 27, 2012): 1250107. http://dx.doi.org/10.1142/s0218216512501076.

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The Torelli group, [Formula: see text], is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface. There are three types of elements that naturally arise in studying [Formula: see text]: bounding pair maps, separating twists, and simply intersecting pair maps (SIP-maps). Historically the first two types of elements have been the focus of the literature on [Formula: see text], while SIP-maps have received relatively little attention until recently, due to an infinite presentation of [Formula: see text] introduced by Putman that uses all three types of elements. We will give a topological characterization of the image of an SIP-map under the Johnson homomorphism and Birman–Craggs–Johnson homomorphism. We will also classify which SIP-maps are in the kernel of these homomorphisms. Then we will look at the subgroup generated by all SIP-maps, SIP (Sg), and show it is an infinite index subgroup of [Formula: see text].
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Sunderrajan, K., M. Suresh, and R. Muthuraj. "Homomorphism and Anti Homomorphism on Multi L-Fuzzy Quotient Group of a Group." International Journal of Mathematics Trends and Technology 23, no. 1 (July 25, 2015): 33–39. http://dx.doi.org/10.14445/22315373/ijmtt-v23p505.

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Dissertations / Theses on the topic "Group homomorphism"

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Slye, Jeffrey. "UNDERGRADUATE MATHEMATICS STUDENTS’ CONNECTIONS BETWEEN THEIR GROUP HOMOMORPHISM AND LINEAR TRANSFORMATION CONCEPT IMAGES." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/65.

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It is well documented that undergraduate students struggle with the more formal and abstract concepts of vector space theory in a first course on linear algebra. Some of these students continue on to classes in abstract algebra, where they learn about algebraic structures such as groups. It is clear to the seasoned mathematician that vector spaces are in fact groups, and so linear transformations are group homomorphisms with extra restrictions. This study explores the question of whether or not students see this connection as well. In addition, I probe the ways in which students’ stated understandings are the same or different across contexts, and how these differences may help or hinder connection making across domains. Students’ understandings are also briefly compared to those of mathematics professors in order to highlight similarities and discrepancies between reality and idealistic expectations. The data for this study primarily comes from clinical interviews with ten undergraduates and three professors. The clinical interviews contained multiple card sorts in which students expressed the connections they saw within and across the domains of linear algebra and abstract algebra, with an emphasis specifically on linear transformations and group homomorphisms. Qualitative data was analyzed using abductive reasoning through multiple rounds of coding and generating themes. Overall, I found that students ranged from having very few connections, to beginning to form connections once placed in the interview setting, to already having a well-integrated morphism schema across domains. A considerable portion of this paper explores the many and varied ways in which students succeeded and failed in making mathematically correct connections, using the language of research on analogical reasoning to frame the discussion. Of particular interest were the ways in which isomorphisms did or did not play a role in understanding both morphisms, how students did not regularly connect the concepts of matrices and linear transformations, and how vector spaces were not fully aligned with groups as algebraic structures.
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Hohlweg, Christophe. "Properties of the Solomon homomorphism of a finite Coxeter group and minimal elements in two-sided cells of the symmetric group." Université Louis Pasteur (Strasbourg) (1971-2008), 2003. http://www.theses.fr/2003STR13246.

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Caprace, Pierre-Emmanuel. ""Abstract" homomorphisms of split Kac-Moody groups." Doctoral thesis, Universite Libre de Bruxelles, 2005. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210962.

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Cette thèse est consacrée à une classe de groupes, appelés groupes de Kac-Moody, qui généralise de façon naturelle les groupes de Lie semi-simples, ou plus précisément, les groupes algébriques réductifs, dans un contexte infini-dimensionnel. On s'intéresse plus particulièrement au problème d'isomorphismes pour ces groupes, en vue d'obtenir un analogue infini-dimensionnel de la célèbre théorie des homomorphismes 'abstraits' de groupes algébriques simples, due à Armand Borel et Jacques Tits.

Le problème d'isomorphismes qu'on étudie s'avère être un cas particulier d'un problème plus général, qui consiste à caractériser les homomorphismes de groupes algébriques vers les groupes de Kac-Moody, dont l'image est bornée. Ce problème peut à son tour s'énoncer comme un problème de rigidité pour les actions de groupes algébriques sur les immeubles, via l'action naturelle d'un groupe de Kac-Moody sur une paire d'immeubles jumelés. Les résultats partiels, relatifs à ce problème de rigidité, que nous obtenons, nous permettent d'apporter une solution complète au problème d'isomorphismes pour les groupes de Kac-Moody déployés.

En particulier, on obtient un résultat de dévissage pour les automorphismes de ces objets. Celui-ci fournit à son tour une description complète de la structure du groupe d'automorphismes d'un groupe de Kac-Moody déployé sur un corps de caractéristique~$0$.

Nos arguments permettent également de traiter de façon analogue certaines formes anisotropes de groupes de Kac-Moody complexes, appelées formes unitaires. On montre en particulier que la topologie Hausdorff naturelle que portent ces formes est un invariant de leur structure de groupe abstrait. Ceci généralise un résultat bien connu de H. Freudenthal pour les groupes de Lie compacts.

Enfin, l'on s'intéresse aux homomorphismes de groupes de Kac-Moody à image fini-dimensionnelle, et l'on démontre la non-existence de tels homomorphismes à noyau central, lorsque le domaine est un groupe de Kac-Moody de type indéfini sur un corps infini. Ceci réduit un problème ouvert, dit problème de linéarité pour les groupes de Kac-Moody, au cas de corps de base finis.
Doctorat en sciences, Spécialisation mathématiques
info:eu-repo/semantics/nonPublished

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Nazzal, Lamies Joureus. "Homomorphic images of semi-direct products." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2770.

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The main purpose of this thesis is to describe methods of constructing computer-free proofs of existence of finite groups and give useful techniques to perform double coset enumeration of groups with symmetric presentations over their control groups.
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Torres, Giese Enrique. "Spaces of homomorphisms and group cohomology." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/224.

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In this work we study the space of group homomorphisms Hom(Γ,G) from a geometric and simplicial point of view. The case in which the source group is a free abelian group of rank n is studied in more detail since this space can be identified with the space of commuting n-tuples of elements from G. This latter case is of particular interest when the target is a Lie group. The simplicial approach allows us to to construct a family of spaces that filters the classifying space of a group by filtering group theoretical information of the given group. Namely, we use the lower central series of free groups to construct a family of simplicial subspaces of the bar construction of the classifying space of a group. The first layer of this filtration is studied in more detail for transitively commutative (TC) groups.
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Vera, Arboleda Anderson Arley. "Homomorphismes de type Johnson pour les surfaces et invariant perturbatif universel des variétés de dimension trois." Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAD009/document.

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Soit Σ une surface compacte connexe orientée avec une seule composante du bord. Notons par M le groupe d'homéotopie de Σ. En considérant l'action de M sur le groupe fondamental de Σ, il est possible de définir différentes filtrations de M ainsi que des homomorphismes sur chaque terme de ces filtrations. Le but de cette thèse est double. En premier lieu, nous étudions deux filtrations de M : la " filtration de Johnson-Levine " introduite par Levine et la " filtration de Johnson alternative " introduite recemment par Habiro et Massuyeau. Les définitions de ces deux filtrations prennent en compte un corps en anses bordé par la surface. Nous nous référons à ces filtrations comme " filtrations de type Johnson " et les homomorphismes correspondants sont appelés " homomorphismes de type Johnson " par leur analogie avec la filtration de Johnson originale et les homomorphismes de Johnson usuels. Nous donnons une comparaison de la filtration de Johnson avec la filtration de Johnson-Levine au niveau du monoïde des cobordismes d'homologie de Σ. Nous donnons également une comparaison entre la filtration de Johnson alternative, la filtration Johnson-Levine et la filtration de Johnson au niveau du groupe d'homéotopie. Deuxièmement, nous étudions la relation entre les " homomorphismes de type Johnson" et l'extension fonctorielle de l'invariant perturbatif universel des variétés de dimension trois (l'invariant de Le-Murakami-Ohtsuki ou invariant LMO). Cette extension fonctorielle s'appelle le foncteur LMO et il prend ses valeurs dans une catégorie de diagrammes. Nous démontrons que les "homomorphismes de type Johnson " peuvent être lus dans la réduction arborée du foncteur LMO. En particulier, cela fournit une nouvelle grille de lecture de la réduction arborée du foncteur LMO
Let Σ be a compact oriented surface with one boundary component and let M denote the mapping class group of Σ. By considering the action of M on the fundamental group of Σ it is possible to define different filtrations of M together with some homomorphisms on each term of the filtrations. The aim of this thesis is twofold. First, we study two filtrations of M : the « Johnson-Levine filtration » introduced by Levine and « the alternative Johsnon filtration » introduced recently by Habiro and Massuyeau. The definition of both filtrations involve a handlebody bounded by Σ. We refer to these filtrations as ≪ Johnson-type filtrations » and the corresponding homomorphisms have referred to as « Johnson-type homomorphisms » by their analogy with the original Johnson filtration and the usual Johnson homomorphisms. We provide a comparison of the Johnson filtration with the Johnson-Levine filtration at the level of the monoid of homology cobordisms of Σ. We also provide a comparison of the alternative Johnson filtration with the Johnson-Levine filtration and the Johnson filtration at the level of the mapping class group. Secondly, we study the relationship between the « Johnson-type homomorphisms » and the functorial extension of the universal perturbative invariant of 3-manifolds (the Le-Murakami-Ohtsuki invariant or LMO invariant). This functorial extension is calling the LMO functor and it takes values in a category of diagrams. We prove that the « Johnson-type homomorphisms » is in the tree reduction of the LMO functor. In particular, this provides a new reading grid of the tree reduction of the LMO functor
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Baccari, Angelica. "Simple Groups, Progenitors, and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/736.

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The foundation of the work of this thesis is based around the involutory progenitor and the finite homomorphic images found therein. This process is developed by Robert T. Curtis and he defines it as 2^{*n} :N {pi w | pi in N, w} where 2^{*n} denotes a free product of n copies of the cyclic group of order 2 generated by involutions. We repeat this process with different control groups and a different array of possible relations to discover interesting groups, such as sporadic, linear, or unitary groups, to name a few. Predominantly this work was produced from transitive groups in 6,10,12, and 18 letters. Which led to identify some appealing groups for this project, such as Janko group J1, Symplectic groups S(4,3) and S(6,2), Mathieu group M12 and some linear groups such as PGL2(7) and L2(11) . With this information, we performed double coset enumeration on some of our findings, M12 over L_2(11) and L_2(31) over D15. We will also prove their isomorphism types with the help of the Jordan-Holder theorem, which aids us in defining the make up of the group. Some examples that we will encounter are the extensions of L_2(31)(center) 2 and A5:2^2.
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Kent, Curtis Andrew. "Homomorphisms into the Fundamental Group of One-Dimensional and Planar Peano Continua." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2452.pdf.

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Farber, Lee. "Symmetric generation of finite homomorphic images?" CSUSB ScholarWorks, 2005. https://scholarworks.lib.csusb.edu/etd-project/2901.

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The purpose of this thesis was to present the technique of double coset enumeration and apply it to construct finite homomorphic images of infinite semidirect products. Several important homomorphic images include the classical groups, the Projective Special Linear group and the Derived Chevalley group were constructed.
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Peim, M. D. "On the K-theory and homotopy groups of #OMEGA# #SIGMA#BU." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257661.

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Books on the topic "Group homomorphism"

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1955-, Moy Allen, and Conference Board of the Mathematical Sciences., eds. Harish-Chandra homomorphisms for p-adic groups. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1985.

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"Abstract'' homomorphisms of split Kac-Moody groups. Providence, R.I: American Mathematical Society, 2009.

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McDuff, Dusa, and Dietmar Salamon. The group of symplectomorphisms. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0011.

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This chapter discusses the basic properties of the group of symplectomorphisms of a compact connected symplectic manifold and its subgroup of Hamiltonian symplectomorphisms. It begins by showing that the group of symplectomorphisms is locally path-connected and then moves on to the flux homomorphism. The main result here is a theorem of Banyaga that characterizes the Hamiltonian symplectomorphisms in terms of the flux homomorphism. In the noncompact case there is another interesting homomorphism, called the Calabi homomorphism, that takes values in the reals and may be defined on the universal cover of the group of Hamiltonian symplectomorphisms. The chapter ends with a brief comparison of the topological properties of the group of symplectomorphisms with those of the group of diffeomorphisms.
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Farb, Benson, and Dan Margalit. Dehn Twists. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0004.

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This chapter deals with Dehn twists, the simplest infinite-order elements of Mod(S). It first defines Dehn twists and proves that they are nontrivial elements of the mapping class group. In particular, it considers the action of Dehn twists on simple closed curves. As one application of this study, the chapter proves that if two simple closed curves in Sɡ have geometric intersection number greater than 1, then the associated Dehn twists generate a free group of rank 2 in Mod(S). It also proves some fundamental facts about Dehn twists and describes the center of the mapping class group, along with algebraic relations that can occur between two Dehn twists. Finally, it explores three geometric operations on a surface that each induces an algebraic operation on the corresponding mapping class group: the inclusion homomorphism, the capping homomorphism, and the cutting homomorphism.
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Farb, Benson, and Dan Margalit. The Symplectic Representation and the Torelli Group. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0007.

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This chapter discusses the basic properties and applications of a symplectic representation, denoted by Ψ‎, and its kernel, called the Torelli group. After describing the algebraic intersection number as a symplectic form, the chapter presents three different proofs of the surjectivity of Ψ‎, each illustrating a different theme. It also illustrates the usefulness of the symplectic representation by two applications to understanding the algebraic structure of Mod(S). First, the chapter explains how this representation is used by Serre to prove the theorem that Mod(Sɡ) has a torsion-free subgroup of finite index. It thens uses the symplectic representation to prove, following Ivanov, the following theorem of Grossman: Mod(Sɡ) is residually finite. It also considers some of the pioneering work of Dennis Johnson on the Torelli group. In particular, a Johnson homomorphism is constructed and some of its applications are given.
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Chamberlain, Robert F. Groups with certain finite homomorphic images cyclic. 1987.

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Boudou, Alain, and Yves Romain. On Product Measures Associated with Stationary Processes. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.15.

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This article considers the connections between product measures and stationary processes. It first provides an overview of historical facts and relevant terminology, basic concepts and the mathematical approach. In particular, it discusses random measures, the projection-valued spectral measure (PVSM), convolution products, and the association between shift operators and PVSMs. It then presents the main results and their first potential applications, focusing on stochastic integrals, the image of a random measure under measurable mapping, the existence of a transport-type theorem, and the transpose of a continuous homomorphism between groups. It also describes the PVSM associated with a unitary operator, the convolution product of two PVSMs, the unitary operators generated by a PVSM, extension of the convolution product of two PVSMs, an equation where the unknown quantity is a PVSM, and the convolution product of two random measures. The article concludes with an analysis of mathematical developments related to the previous results.
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Book chapters on the topic "Group homomorphism"

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Raskhodnikova, Sofya, and Ronitt Rubinfeld. "Linearity and Group Homomorphism Testing/Testing Hadamard Codes." In Encyclopedia of Algorithms, 1–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-642-27848-8_202-2.

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Nuida, Koji. "Towards Constructing Fully Homomorphic Encryption without Ciphertext Noise from Group Theory." In International Symposium on Mathematics, Quantum Theory, and Cryptography, 57–78. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5191-8_8.

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Abstract In CRYPTO 2008, 1 year earlier than Gentry’s pioneering “bootstrapping” technique for the first fully homomorphic encryption (FHE) scheme, Ostrovsky and Skeith III had suggested a completely different approach towards achieving FHE. They showed that the $$\mathsf {NAND}$$ operator can be realized in some non-commutative groups; consequently, homomorphically encrypting the elements of the group will yield an FHE scheme, without ciphertext noise to be bootstrapped. However, no observations on how to homomorphically encrypt the group elements were presented in their paper, and there have been no follow-up studies in the literature. The aim of this paper is to exhibit more clearly what is sufficient and what seems to be effective for constructing FHE schemes based on their approach. First, we prove that it is sufficient to find a surjective homomorphism $$\pi :\widetilde{G} \rightarrow G$$ between finite groups for which bit operators are realized in G and the elements of the kernel of $$\pi $$ are indistinguishable from the general elements of $$\widetilde{G}$$. Secondly, we propose new methodologies to realize bit operators in some groups G. Thirdly, we give an observation that a naive approach using matrix groups would never yield secure FHE due to an attack utilizing the “linearity” of the construction. Then we propose an idea to avoid such “linearity” by using combinatorial group theory. Concretely realizing FHE schemes based on our proposed framework is left as a future research topic.
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Valenza, Robert J. "Groups and Group Homomorphisms." In Linear Algebra, 18–36. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0901-0_2.

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Hibbard, Allen C., and Kenneth M. Levasseur. "Group Homomorphisms." In Exploring Abstract Algebra With Mathematica®, 101–10. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1530-1_13.

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Birken, Philipp. "Group Homomorphisms." In Student Solutions Manual, 50–54. 10th ed. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003182306-11.

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Fuchs, László. "Homomorphism Groups." In Springer Monographs in Mathematics, 213–28. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19422-6_7.

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Green, James Alexander. "Homomorphisms." In Sets and groups, 87–109. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-011-6095-7_7.

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San Martin, Luiz A. B. "Homomorphisms and Coverings." In Lie Groups, 145–62. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61824-7_7.

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Rotman, Joseph J. "Groups and Homomorphisms." In Graduate Texts in Mathematics, 1–19. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4176-8_1.

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Johnson, Kenneth W. "K-Characters and n-Homomorphisms." In Group Matrices, Group Determinants and Representation Theory, 271–86. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28300-1_8.

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Conference papers on the topic "Group homomorphism"

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Khots, Boris, and Dmitriy Khots. "The spin-1 equivalent homomorphism of group SU(2) to group SO(3) from observer’s mathematics point of view." In Spintronics XIV, edited by Henri-Jean M. Drouhin, Jean-Eric Wegrowe, and Manijeh Razeghi. SPIE, 2021. http://dx.doi.org/10.1117/12.2591817.

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Xu, Chuan-Yu. "Homomorphism of Intuitionistic Fuzzy Groups." In Sixth International Conference on Machine Learning Cybernetics. IEEE, 2007. http://dx.doi.org/10.1109/icmlc.2007.4370322.

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Shpilka, Amir, and Avi Wigderson. "Derandomizing homomorphism testing in general groups." In the thirty-sixth annual ACM symposium. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/1007352.1007421.

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Colón, Diego. "Cartan’s Connection, Fiber Bundles and Quaternions in Kinematics and Dynamics Calculations." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46758.

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Abstract:
It is used the concept of Cartan’s connection and principal fiber bundles to obtain formulas for kinematics and dynamics calculations for robotic manipulators. A principal fiber bundle is a differentiable manifold formed by a base space B (in this case ℝ3)) plus all possible reference frames attached to a point p ∈ B (that is the fiber Sp). Cartan’s connections are the most general way to represent velocity of frames. In previous works, those ideas were applied to fiber bundles with fibers homomorphic to the Lie group SO(3) (or SE(3)). In this paper, it is applied to the case of fibers homomorphic either to the group SU(2) (for rotational motion) or to the group of unit dual quaternions (for translational plus rotational motion). It is also presented some results of calculations, and indicate future directions for research.
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Xiufeng, Chang, Hai Jinke, and Huang Xurong. "Some properties on the homomorphism of groups." In The 2nd Information Technology and Mechatronics Engineering Conference (ITOEC 2016). Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/itoec-16.2016.43.

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Dinur, Irit, Elena Grigorescu, Swastik Kopparty, and Madhu Sudan. "Decodability of group homomorphisms beyond the johnson bound." In the 40th annual ACM symposium. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1374376.1374418.

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Li, Hua, and Edwin K. P. Chong. "On Connections between Group Homomorphisms and the Ingleton Inequality." In 2007 IEEE International Symposium on Information Theory. IEEE, 2007. http://dx.doi.org/10.1109/isit.2007.4557514.

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Li, Peili, and Haixia Xu. "Homomorphic Signatures for Correct Computation of Group Elements." In 2013 Fourth International Conference on Emerging Intelligent Data and Web Technologies (EIDWT). IEEE, 2013. http://dx.doi.org/10.1109/eidwt.2013.16.

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KITANO, Teruaki, and Masaaki SUZUKI. "ON THE EXISTENCE OF A SURJECTIVE HOMOMORPHISM BETWEEN KNOT GROUPS." In Intelligence of Low Dimensional Topology 2006 - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770967_0022.

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POLÁK, L. "LITERAL VARIETIES AND PSEUDOVARIETIES OF HOMOMORPHISMS ONTO ABELIAN GROUPS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708700_0018.

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