Relevant bibliographies by topics / CHARACTER THEORY, FINITE GROUPS

Academic literature on the topic 'CHARACTER THEORY, FINITE GROUPS'

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Published: 10 March 2023

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Journal articles on the topic "CHARACTER THEORY, FINITE GROUPS"

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Boyer, Robert. "Character theory of infinite wreath products." International Journal of Mathematics and Mathematical Sciences 2005, no. 9 (2005): 1365–79. http://dx.doi.org/10.1155/ijmms.2005.1365.

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The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” TheK0-invariant of the groupC∗-algebra is also determined.
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Isaacs, I. M. "The π-character theory of solvable groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, no. 1 (August 1994): 81–102. http://dx.doi.org/10.1017/s1446788700036077.

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AbstractThere is a deeper structure to the ordinary character theory of finite solvable groups than might at first be apparent. Mauch of this structure, which has no analog for general finite gruops, becomes visible onyl when the character of solvable groups are viewes from the persepective of a particular set π of prime numbers. This purely expository paper discusses the foundations of this πtheory and a few of its applications. Included are the definitions and essential properties of Gajendragadkar's π-special characters and their connections with the irreducible πpartial characters and their associated Fong characters. Included among the consequences of the theory discussed here are applications to questions about the field generated by the values of a character, about extensions of characters of subgroups and about M-groups.
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Isaacs, I. M. "Book Review: Character theory of finite groups." Bulletin of the American Mathematical Society 36, no. 04 (July 22, 1999): 489–93. http://dx.doi.org/10.1090/s0273-0979-99-00789-2.

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Ikeda, Kazuoki. "Character Values of Finite Groups." Algebra Colloquium 7, no. 3 (August 2000): 329–33. http://dx.doi.org/10.1007/s10011-000-0329-1.

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Chetard, Béatrice I. "Graded character rings of finite groups." Journal of Algebra 549 (May 2020): 291–318. http://dx.doi.org/10.1016/j.jalgebra.2019.11.041.

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Schmid, Peter. "Finite groups satisfying character degree congruences." Journal of Group Theory 21, no. 6 (November 1, 2018): 1073–94. http://dx.doi.org/10.1515/jgth-2018-0019.

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Abstract Let G be a finite group, p a prime and {c\in\{0,1,\ldots,p-1\}} . Suppose that the degree of every nonlinear irreducible character of G is congruent to c modulo p. If here {c=0} , then G has a normal p-complement by a well known theorem of Thompson. We prove that in the cases where {c\neq 0} the group G is solvable with a normal abelian Sylow p-subgroup. If {p\neq 3} then this is true provided these character degrees are congruent to c or to {-c} modulo p.
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Xiong, Huan. "Finite Groups Whose Character Graphs Associated with Codegrees Have No Triangles." Algebra Colloquium 23, no. 01 (January 6, 2016): 15–22. http://dx.doi.org/10.1142/s1005386716000031.

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Motivated by Problem 164 proposed by Y. Berkovich and E. Zhmud' in their book “Characters of Finite Groups”, we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind of character graphs of finite groups associated with codegrees. Such graphs have close and obvious connections with character codegree graphs. For example, they have the same number of connected components. By analogy with the work of finite groups whose character graphs (associated with degrees) have no triangles, we conduct a result of classifying finite groups whose character graphs associated with codegrees have no triangles in the latter part of this paper.
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Madanha, Sesuai Yash. "Zeros of primitive characters of finite groups." Journal of Group Theory 23, no. 2 (March 1, 2020): 193–216. http://dx.doi.org/10.1515/jgth-2019-2051.

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AbstractWe classify finite non-solvable groups with a faithful primitive irreducible complex character that vanishes on a unique conjugacy class. Our results answer a question of Dixon and Rahnamai Barghi and suggest an extension of Burnside’s classical theorem on zeros of characters.
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Qian, Guohua. "Finite groups with consecutive nonlinear character degrees." Journal of Algebra 285, no. 1 (March 2005): 372–82. http://dx.doi.org/10.1016/j.jalgebra.2004.11.021.

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Chillag, David, and Marcel Herzog. "Finite groups with almost distinct character degrees." Journal of Algebra 319, no. 2 (January 2008): 716–29. http://dx.doi.org/10.1016/j.jalgebra.2005.07.039.

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Dissertations / Theses on the topic "CHARACTER THEORY, FINITE GROUPS"

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McHugh, John. "Monomial Characters of Finite Groups." ScholarWorks @ UVM, 2016. http://scholarworks.uvm.edu/graddis/572.

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An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters – those induced from a linear character of some subgroup – since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the class of M-groups, those groups all of whose irreducible characters are monomial. A classical theorem of Taketa asserts that an M-group is necessarily solvable, and Dade proved that every solvable group can be embedded as a subgroup of an M-group. After discussing results related to M-groups, we will construct explicit families of solvable groups that cannot be embedded as subnormal subgroups of any M-group. We also discuss groups possessing a unique non-monomial irreducible character, and prove that such a group cannot be simple.
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Doyle, Michael Patrick. "Partitioning the Set of Subgroups of a Finite Group Using Thompson's Generalized Characters." Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1428594171.

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Baccari, Charles. "Investigation of Finite Groups Through Progenitors." CSUSB ScholarWorks, 2017. https://scholarworks.lib.csusb.edu/etd/600.

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The goal of this presentation is to find original symmetric presentations of finite groups. It is frequently the case, that progenitors factored by appropriate relations produce simple and even sporadic groups as homomorphic images. We have discovered two of the twenty-six sporadic simple groups namely, M12, J1 and the Lie type group Suz(8). In addition several linear and classical groups will also be presented. We will present several progenitors including: 2*12: 22 x (3 : 2), 2*11: PSL2(11), 2*5: (5 : 4) which have produced the homomorphic images: M12 : 2, Suz(8) x 2, and J1 x 2. We will give monomial progenitors whose homomorphic images are: 17*10 :m PGL2(9), 3*4:m Z2 ≀D4 , and 13*2:m (22 x 3) : 2 which produce the homomorphic images:132 : ((2 x 13) : (2 x 3)), 2 x S9, and (22)•PGL4(3). Once we have a presentation of a group we can verify the group's existence through double coset enumeration. We will give proofs of isomorphism types of the presented images: S3 x PGL2(7) x S5, 28:A5, and 2•U4(2):2.
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Ward, David Charles. "Topics in finite groups : homology groups, pi-product graphs, wreath products and cuspidal characters." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/topics-in-finite-groups-homology-groups-piproduct-graphs-wreath-products-and-cuspidal-characters(7e90d219-fba7-4ff0-9071-c624acab7aaf).html.

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Prins, A. L. "Fischer-clifford matrices and character tables of inertia groups of maximal subgroups of finite simple groups of extension type." University of the Western Cape, 2011. http://hdl.handle.net/11394/5430.

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Philosophiae Doctor - PhD
The aim of this dissertation is to calculate character tables of group extensions. There are several well–developed methods for calculating the character tables of group extensions. In this dissertation we study the method developed by Bernd Fischer, the so–called Fischer–Clifford matrices method, which derives its fundamentals from the Clifford theory. We consider only extensions G of the normal subgroup K by the subgroup Q with the property that every irreducible character of K can be extended to an irreducible character of its inertia group in G, if K is abelian. This is indeed the case if G is a split extension, by a well-known theorem of Mackey. A brief outline of the classical theory of characters pertinent to this study, is followed by a discussion on the calculation of the conjugacy classes of extension groups by the method of coset analysis. The Clifford theory which provide the basis for the theory of Fischer-Clifford matrices is discussed in detail. Some of the properties of these Fischer-Clifford matrices which make their calculation much easier are also given. As mentioned earlier we restrict ourselves to split extension groups G in which K is always elementary abelian. In this thesis we are concerned with the construction of the character tables of certain groups which are associated with Fi₂₂ and Sp₈ (2). Both of these groups have a maximal subgroup of the form 2⁷: Sp₆ (2) but they are not isomorphic to each other. In particular we are interested in the inertia groups of these maximal subgroups, which are split extensions. We use the technique of the Fischer-Clifford matrices to construct the character tables of these inertia groups. These inertia groups of 2⁷ : Sp₆(2), the maximal subgroup of Fi₂₂, are 2⁷ : S₈, 2⁷ : Ο⁻₆(2) and 2⁷ : (2⁵ : S₆). The inertia group of 2⁷ : Sp₆(2), the affine subgroup of Sp₈(2), is 2⁷ : (2⁵ : S₆) which is not isomorphic to the group with the same form which was mentioned earlier.
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Nenciu, Adriana. "Character tables of finite groups." [Gainesville, Fla.] : University of Florida, 2006. http://purl.fcla.edu/fcla/etd/UFE0014824.

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Skabelund, Dane Christian. "Character Tables of Metacyclic Groups." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/3913.

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We show that any two split metacyclic groups with the same character tables are isomorphic. We then use this to show that among metacyclic groups that are either 2-groups or are of odd order divisible by at most two primes, that the dihedral and generalized quaternion groups of order 2^n, n = 3, are the only pairs that have the same character tables.
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Davies, Ryan. "An induction theorem inspired by Brauer's induction theorem for characters of finite groups." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8834/.

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Brauer's induction theorem states that every irreducible character of a finite group G can be expressed as an integral linear combination of induced characters from elementary subgroups. The goal of this thesis is to develop our own induction theorem inspired by both Brauer's induction theorem and Global-Local conjectures. Specifically we replace the set of elementary subgroups of G by the set of subgroups of index divisible by the prime power divisors of the given character's degree. We aim to do this by using a reduction theorem to almost simple and quasisimple groups, using the Classification of Finite Simple Groups to deal with the remaining cases.
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Taylor, Paul Anthony. "Computational investigation into finite groups." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/computational-investigation-into-finite-groups(8fe69098-a2d0-4717-b8d3-c91785add68c).html.

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We briefly discuss the algorithm given in [Bates, Bundy, Perkins, Rowley, J. Algebra, 316(2):849-868, 2007] for determining the distance between two vertices in a commuting involution graph of a symmetric group.We develop the algorithm in [Bates, Rowley, Arch. Math. (Basel), 85(6):485-489, 2005] for computing a subgroup of the normalizer of a 2-subgroup X in a finite group G, examining in particular the issue of when to terminate the randomized procedure. The resultant algorithm is capable of handling subgroups X of order up to 512 and is suitable, for example, for matrix groups of large degree (an example calculation is given using 112x112 matrices over GF(2)).We also determine the suborbits of conjugacy classes of involutions in several of the sporadic simple groups?namely Janko's group J4, the Fischer sporadic groups, and the Thompson and Harada-Norton groups. We use our results to determine the structure of some graphs related to this data.We include implementations of the algorithms discussed in the computer algebra package MAGMA, as well as representative elements for the involution suborbits.
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Cassell, Eleanor Jane. "Conjugacy classes in finite groups, commuting graphs and character degrees." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4628/.

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In the first half of this thesis we determine the connectivity of commuting graphs of conjugacy classes of semisimple and some unipotent elements in GL(n,q). In the second half we prove that the degree of an irreducible character of a finite simple group divides the size of some conjugacy class of the group.
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Books on the topic "CHARACTER THEORY, FINITE GROUPS"

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Lewis, Mark L., Gabriel Navarro, Donald S. Passman, and Thomas R. Wolf, eds. Character Theory of Finite Groups. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/conm/524.

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Character theory of finite groups. Providence, R.I: AMS Chelsea Pub., 2006.

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Isaacs, I. Martin. Character theory of finite groups. New York: Dover, 1994.

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Huppert, Bertram. Character theory of finite groups. Berlin: Walter de Gruyter, 1998.

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Navarro, G. Characters and blocks of finite groups. Cambridge, UK: Cambridge University Press, 1998.

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Character theory for the odd order theorem. Cambridge: Cambridge University Press, 2000.

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Riehm, C. R. Introduction to orthogonal, symplectic, and unitary representations of finite groups. Providence, R.I: American Mathematical Society, 2011.

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The classification of finite simple groups: Groups of characteristic 2 type. Providence, R.I: American Mathematical Society, 2011.

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Character theory of finite groups: Conference in honor of I. Martin Isaacs, June 3-5, 2009, Universitat de Valencia, Valencia, Spain. Providence, R.I: American Mathematical Society, 2010.

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Finite group theory. Cambridge [Cambridgeshire]: Cambridge University Press, 1986.

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Book chapters on the topic "CHARACTER THEORY, FINITE GROUPS"

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Turull, A. "Character Theory and Length Problems." In Finite and Locally Finite Groups, 377–400. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0329-9_14.

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Schneider, Peter. "The Brauer Character." In Modular Representation Theory of Finite Groups, 87–96. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4832-6_3.

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Steinberg, Benjamin. "Character Theory and the Orthogonality Relations." In Representation Theory of Finite Groups, 27–50. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0776-8_4.

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Manz, Olaf. "Some new developments and open questions in the character theory of finite groups." In Representation Theory of Finite Groups and Finite-Dimensional Algebras, 461–76. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-8658-1_21.

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Isaacs, I. M. "Partial characters of π-separable groups." In Representation Theory of Finite Groups and Finite-Dimensional Algebras, 273–87. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-8658-1_10.

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Dolfi, Silvio, Emanuele Pacifici, and Lucia Sanus. "On Zeros of Characters of Finite Groups." In Group Theory and Computation, 41–58. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2047-7_3.

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Kessar, Radha, and Markus Linckelmann. "Descent of Equivalences and Character Bijections." In Geometric and Topological Aspects of the Representation Theory of Finite Groups, 181–212. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94033-5_7.

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Sengupta, Ambar N. "Character Duality." In Representing Finite Groups, 267–79. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-1231-1_10.

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Sambale, Benjamin. "Blocks with Few Characters." In Blocks of Finite Groups and Their Invariants, 219–27. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12006-5_15.

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Kurzweil, Hans, and Bernd Stellmacher. "Groups Acting on Groups." In The Theory of Finite Groups, 175–223. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/0-387-21768-1_8.

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Conference papers on the topic "CHARACTER THEORY, FINITE GROUPS"

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Nikitina, A. A. "Finite groups with an almost large irreducible character." In XX Anniversary All-Russian Scientific and Practical Conference of Young Scientists, Postgraduates and Students. Technical Institute (BRANCH) of NEFU, 2019. http://dx.doi.org/10.18411/s-2019-91.

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Coquereaux, Robert. "Character tables (modular data) for Drinfeld doubles of finite groups." In 7th International Conference on Mathematical Methods in Physics. Trieste, Italy: Sissa Medialab, 2013. http://dx.doi.org/10.22323/1.175.0024.

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Pillay, Anand. "Finite-dimensional differential algebraic groups and the Picard-Vessiot theory." In Differential Galois Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc58-0-14.

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Radulescu, Andrei, Robert Calderbank, and Stuart Schwartz. "Full-Diversity Finite-Constellation 4 x 4 Differential STBC Based on Finite Quaternion Groups." In 2006 IEEE Information Theory Workshop. IEEE, 2006. http://dx.doi.org/10.1109/itw.2006.322856.

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Poiseeva, Sargylana S. "A bound on the order of finite groups with large irreducible character." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON CONSTRUCTION AND BUILDING ENGINEERING (ICONBUILD) 2017: Smart Construction Towards Global Challenges. Author(s), 2017. http://dx.doi.org/10.1063/1.5012675.

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Radulescu, Andrei D., Robert A. Calderbank, and Stuart C. Schwartz. "Full-Diversity Finite-Constellation 4 x 4 Differential STBC Based on Finite Quaternion Groups." In 2006 IEEE Information Theory Workshop - ITW '06 Chengdu. IEEE, 2006. http://dx.doi.org/10.1109/itw2.2006.323838.

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Biglieri, Ezio, Emanuele Viterbo, and Michele Elia. "Error Control of Line Codes Generated by Finite Coxeter Groups." In 2018 Information Theory and Applications Workshop (ITA). IEEE, 2018. http://dx.doi.org/10.1109/ita.2018.8503222.

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HIRAI, TAKESHI, and ETSUKO HIRAI. "CHARACTER FORMULA FOR WREATH PRODUCTS OF FINITE GROUPS WITH THE INFINITE SYMMETRIC GROUP." In Proceedings of the Third German-Japanese Symposium. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701503_0008.

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Guo, Wenbin, Vasilii G. Safonov, and Alexander N. Skiba. "On Some Constructions and Results of the Theory of Partially Soluble Finite Groups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0019.

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Adcock, Thomas A. A., and Shiqiang Yan. "The Focusing of Uni-Directional Gaussian Wave-Groups in Finite Depth: An Approximate NLSE Based Approach." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20993.

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The non-linear changes to a NewWave type wave-group are helpful in developing our understanding of the non-linear interactions which can lead to the formation of freak waves. In addition, Gaussian wave-groups are used in model tests where it is useful to have a simple model for their non-linear dynamics. This paper derives a simple analytical model to describe the nonlinear changes to a wave-group as it focuses. This paper is an extension to finite depth of the theory developed for deep water in Adcock & Taylor (2009) (Proc. Roy. Soc. A 465(2110)). The model is derived using the conserved quantities of the cubic nonlinear Schrodinger equation (NLSE). In deep water there are substantial changes to the group shape and spectrum as the wave-group focuses, and the characteristics of these changes are governed by the Benjamin-Feir Index. However, in finite depth the characteristics of the non-linear interactions change, reducing the non-linear changes to the group shape. The analytical model is validated against simulations using the NLSE and against full potential flow solutions using a QALE-FEM numerical scheme. We also compare its predictions against experiments in a physical wavetank. We find that the NLSE, and thus analytical theories derived from it, capture the dominant physics in the evolution of narrowbanded wave-groups.
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