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Journal articles on the topic 'Group actions'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Tsai, Jessica Chia-Chin, Natalie Sebanz, and Günther Knoblich. "The GROOP effect: Groups mimic group actions." Cognition 118, no. 1 (2011): 135–40. http://dx.doi.org/10.1016/j.cognition.2010.10.007.

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2

Gayathri, K. S. and M. Rajeshwari∗ Mahalakshmi. "Group Actions of wreath product −→Sn on permutation groups." Scandinavian Journal of Information Systems 35, no. 1 (2023): 733–48. https://doi.org/10.5281/zenodo.7807470.

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Wreath product −→Sn = Z2 o Sn of type Bn is a subgroup of the symmetric group S2n. In this paper we determine the group actions of wreath product −→Sn on a finite set. Stabilizer and orbit of a point, imprimitivity of −→Snarealsodiscussed. Also the same is illustrated with an application for n = 3

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3

CARBONE, LISA, and ELIYAHU RIPS. "RECONSTRUCTING GROUP ACTIONS." International Journal of Algebra and Computation 23, no. 02 (2013): 255–323. http://dx.doi.org/10.1142/s021819671340002x.

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We give a general structure theory for reconstructing non-trivial group actions on sets without any further assumptions on the group, the action, or the set on which the group acts. Using certain "local data" [Formula: see text] from the action we build a group [Formula: see text] of the data and a space [Formula: see text] with an action of [Formula: see text] on [Formula: see text] that arise naturally from the data [Formula: see text]. We use these to obtain an approximation to the original group G, the original space X and the original action G × X → X. The data [Formula: see text] is dist

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4

Müller, Gerd. "Deformations of reductive group actions." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 1 (1989): 77–88. http://dx.doi.org/10.1017/s0305004100067992.

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Consider actions of a reductive complex Lie group G on an analytic space germ (X, 0). In a previous paper [16] we proved that such an action is determined uniquely (up to conjugation with an automorphism of (X, 0)) by the induced action of G on the tangent space of (X, 0). Here it will be shown that every deformation of such an action, parametrized holomorphically by a reduced analytic space germ, is trivial, i.e. can be obtained from the given action by conjugation with a family of automorphisms of (X, 0) depending holomorphically on the parameter. (For a more precise formulation in terms of

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5

Yalçin, Ergün. "Group actions and group extensions." Transactions of the American Mathematical Society 352, no. 6 (2000): 2689–700. http://dx.doi.org/10.1090/s0002-9947-00-02485-5.

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6

Johnson, F. E. A. "Extending group actions by finite groups. I." Topology 31, no. 2 (1992): 407–20. http://dx.doi.org/10.1016/0040-9383(92)90030-l.

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7

MEGRELISHVILI, MICHAEL. "Free Topological Groups over (Semi) Group Actions." Annals of the New York Academy of Sciences 788, no. 1 General Topol (1996): 164–69. http://dx.doi.org/10.1111/j.1749-6632.1996.tb36808.x.

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8

Kennison, John F. "Pro-group actions and fundamental pro-groups." Journal of Pure and Applied Algebra 66, no. 2 (1990): 185–218. http://dx.doi.org/10.1016/0022-4049(90)90084-u.

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9

Halacheva, Iva, Anthony Licata, Ivan Losev, and Oded Yacobi. "Categorical braid group actions and cactus groups." Advances in Mathematics 429 (September 2023): 109190. http://dx.doi.org/10.1016/j.aim.2023.109190.

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10

Chen, Liang Yun, Tian Qi Feng, Yao Ma, Ripan Saha, and Hong Yi Zhang. "On Hom-groups and Hom-group Actions." Acta Mathematica Sinica, English Series 39, no. 10 (2023): 1887–906. http://dx.doi.org/10.1007/s10114-023-2133-7.

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11

Fedorova, M. "Faithful group actions and Schreier graphs." Carpathian Mathematical Publications 9, no. 2 (2018): 202–7. http://dx.doi.org/10.15330/cmp.9.2.202-207.

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Each action of a finitely generated group on a set uniquely defines a labelled directed graph called the Schreier graph of the action. Schreier graphs are used mainly as a tool to establish geometrical and dynamical properties of corresponding group actions. In particilar, they are widely used in order to check amenability of different classed of groups. In the present paper Schreier graphs are utilized to construct new examples of faithful actions of free products of groups. Using Schreier graphs of group actions a sufficient condition for a group action to be faithful is presented. This resu

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12

Chiswell, I. M. "Minimal group actions on Λ-trees". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, № 1 (1998): 23–36. http://dx.doi.org/10.1017/s030821050002713x.

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We consider the existence and uniqueness of minimal invariant subtrees for abelian actions of groups on Λ-trees, and whether or not a minimal action is determined up to isomorphism by the hyperbolic length function. The main emphasis is on actions of end type. For a trivial action of end type, there is no minimal invariant subtree. However, if a finitely generated group has an action of end type, the action is nontrivial and there is a unique minimal invariant subtree. There are examples of infinitely generated groups with a nontrivial action of end type for which there is no minimal invariant

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13

Kolganova, Alla. "Chaotic group actions." Bulletin of the Australian Mathematical Society 56, no. 1 (1997): 165–67. http://dx.doi.org/10.1017/s0004972700030847.

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14

Oh, Ju-Mok. "Fuzzified group actions." Soft Computing 23, no. 24 (2019): 12981–89. http://dx.doi.org/10.1007/s00500-019-04261-3.

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15

Ben Yaacov, Itaï, and Julien Melleray. "Isometrisable group actions." Proceedings of the American Mathematical Society 144, no. 9 (2016): 4081–88. http://dx.doi.org/10.1090/proc/13018.

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16

Rosenblatt, Joseph. "Ergodic group actions." Archiv der Mathematik 47, no. 3 (1986): 263–69. http://dx.doi.org/10.1007/bf01192003.

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17

Shi, Enhui, Lizhen Zhou, and Youcheng Zhou. "Chaotic group actions." Applied Mathematics-A Journal of Chinese Universities 18, no. 1 (2003): 59–63. http://dx.doi.org/10.1007/s11766-003-0084-4.

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18

Wasserman, Arthur G. "Simplifying group actions." Topology and its Applications 75, no. 1 (1997): 13–31. http://dx.doi.org/10.1016/s0166-8641(96)00084-3.

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19

Gonçalves, Daniel. "Simplicity of Partial Skew Group Rings of Abelian Groups." Canadian Mathematical Bulletin 57, no. 3 (2014): 511–19. http://dx.doi.org/10.4153/cmb-2014-011-1.

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AbstractLet A be a ring with local units, E a set of local units for A, G an abelian group, and α a partial action of G by ideals of A that contain local units. We show that A*αG is simple if and only if A is G-simple and the center of the corner eδ0(A*αGe)eδ0 is a field for all e ∊ E. We apply the result to characterize simplicity of partial skew group rings in two cases, namely for partial skew group rings arising from partial actions by clopen subsets of a compact set and partial actions on the set level.

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20

DEELEY, ROBIN J., and KAREN R. STRUNG. "Group actions on Smale space -algebras." Ergodic Theory and Dynamical Systems 40, no. 9 (2019): 2368–98. http://dx.doi.org/10.1017/etds.2019.11.

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Group actions on a Smale space and the actions induced on the $\text{C}^{\ast }$-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a mixing Smale space produces a strongly outer action on the homoclinic algebra. We then show that for irreducible Smale spaces, the property of finite Rokhlin dimension passes from the induced action on the homoclinic algebra to the induced actions on the stable and unstable $\text{C}^{\ast }$-algebras. In each of these cases, we discuss the preservation of properties (such as finite nuclear dimensi

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21

Iyer, Ganesh, and Hema Yoganarasimhan. "Strategic Polarization in Group Interactions." Journal of Marketing Research 58, no. 4 (2021): 782–800. http://dx.doi.org/10.1177/00222437211016389.

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The authors study the phenomenon of strategic group polarization, in which members take more extreme actions than their preferences. The analysis is relevant for a broad range of formal and informal group settings, including social media, online platforms, sales teams, corporate and academic committees, and political action committees. In the model, agents with private preferences choose a public action (voice opinions), and the mean of their actions represents the group’s realized outcome. The agents face a trade-off between influencing the group decision and truth-telling. In a simultaneous-

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22

Abbott, Carolyn, David Hume, and Denis Osin. "Extending group actions on metric spaces." Journal of Topology and Analysis 12, no. 03 (2018): 625–65. http://dx.doi.org/10.1142/s1793525319500584.

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We address the following natural extension problem for group actions: Given a group [Formula: see text], a subgroup [Formula: see text], and an action of [Formula: see text] on a metric space, when is it possible to extend it to an action of the whole group [Formula: see text] on a (possibly different) metric space? When does such an extension preserve interesting properties of the original action of [Formula: see text]? We begin by formalizing this problem and present a construction of an induced action which behaves well when [Formula: see text] is hyperbolically embedded in [Formula: see te

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23

Ramsay, Arlan. "Measurable group actions are essentially Borel actions." Israel Journal of Mathematics 51, no. 4 (1985): 339–46. http://dx.doi.org/10.1007/bf02764724.

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24

Suksumran, Teerapong. "Gyrogroup actions: A generalization of group actions." Journal of Algebra 454 (May 2016): 70–91. http://dx.doi.org/10.1016/j.jalgebra.2015.12.033.

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25

Sharma, Ram Parkash, Anu, and Nirmal Singh. "PARTIAL GROUP ACTIONS ON SEMIALGEBRAS." Asian-European Journal of Mathematics 05, no. 04 (2012): 1250060. http://dx.doi.org/10.1142/s179355711250060x.

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For defining a K-semialgebra A, we use Katsov's tensor product which makes the category K-Smod monoidal. Further, if A is a K-semialgebra then AΔ is a KΔ-algebra and A embeds in AΔ. The subtractive and strong partial actions of a group are defined on A. A subtractive partial action α of a group G on A can be extended to a partial action of G on AΔ which helps in globalization of α. A strong partial action on A has a unique subtractive globalization. We also discuss the associativity of the skew group semiring A ×α G.

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26

Zimmer, Robert J. "Groups generating transversals to semisimple lie group actions." Israel Journal of Mathematics 73, no. 2 (1991): 151–59. http://dx.doi.org/10.1007/bf02772946.

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27

Humphries, Stephen P. "Finite Hurwitz braid group actions for Artin groups." Israel Journal of Mathematics 143, no. 1 (2004): 189–222. http://dx.doi.org/10.1007/bf02803499.

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28

Wilking, Burkhard. "Rigidity of group actions on solvable Lie groups." Mathematische Annalen 317, no. 2 (2000): 195–237. http://dx.doi.org/10.1007/s002089900091.

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29

Br�stle, T., G. R�hrle, and L. Hille. "Finiteness for parabolic group actions in classical groups." Archiv der Mathematik 76, no. 2 (2001): 81–87. http://dx.doi.org/10.1007/s000130050545.

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30

KELLENDONK, J., and MARK V. LAWSON. "PARTIAL ACTIONS OF GROUPS." International Journal of Algebra and Computation 14, no. 01 (2004): 87–114. http://dx.doi.org/10.1142/s0218196704001657.

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A partial action of a group G on a set X is a weakening of the usual notion of a group action: the function G×X→X that defines a group action is replaced by a partial function; in addition, the existence of g·(h·x) implies the existence of (gh)·x, but not necessarily conversely. Such partial actions are extremely widespread in mathematics, and the main aim of this paper is to prove two basic results concerning them. First, we obtain an explicit description of Exel's universal inverse semigroup [Formula: see text], which has the property that partial actions of the group G give rise to actions

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31

Godinho, Leonor, and M. E. Sousa-Dias. "The Fundamental Group ofS1-manifolds." Canadian Journal of Mathematics 62, no. 5 (2010): 1082–98. http://dx.doi.org/10.4153/cjm-2010-053-3.

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AbstractWe address the problem of computing the fundamental group of a symplecticS1-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a HamiltonianS1-action. Several examples are presented to illustrate our main results.

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32

MELNIKOV, ALEXANDER, and ANTONIO MONTALBÁN. "COMPUTABLE POLISH GROUP ACTIONS." Journal of Symbolic Logic 83, no. 2 (2018): 443–60. http://dx.doi.org/10.1017/jsl.2017.68.

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AbstractUsing methods from computable analysis, we establish a new connection between two seemingly distant areas of logic: computable structure theory and invariant descriptive set theory. We extend several fundamental results of computable structure theory to the more general setting of topological group actions. As we will see, the usual action of ${S_\infty }$ on the space of structures in a given language is effective in a certain algorithmic sense that we need, and ${S_\infty }$ itself carries a natural computability structure (to be defined). Among other results, we give a sufficient co

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33

Blanc, David, and Debasis Sen. "Realizing homotopy group actions." Bulletin of the Belgian Mathematical Society - Simon Stevin 21, no. 4 (2014): 685–710. http://dx.doi.org/10.36045/bbms/1414091009.

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34

Greenberg, Peter. "Pseudogroups from Group Actions." American Journal of Mathematics 109, no. 5 (1987): 893. http://dx.doi.org/10.2307/2374493.

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35

Kanai, Masahiko. "Rigidity of group actions." Séminaire de théorie spectrale et géométrie 15 (1997): 203–5. http://dx.doi.org/10.5802/tsg.192.

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36

Huru, Hilja L., and Valentin V. Lychagin. "Quantizations of Group Actions." Journal of Generalized Lie Theory and Applications 6 (2012): 1–15. http://dx.doi.org/10.4303/jglta/g120403.

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37

McCullough, Darryl, Andy Miller, and Bruno Zimmermann. "Group Actions on Handlebodies." Proceedings of the London Mathematical Society s3-59, no. 2 (1989): 373–416. http://dx.doi.org/10.1112/plms/s3-59.2.373.

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38

Fisher, David. "Deformations of group actions." Transactions of the American Mathematical Society 360, no. 01 (2008): 491–506. http://dx.doi.org/10.1090/s0002-9947-07-04372-3.

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39

Radcliffe, A. J., and A. D. Scott. "Reconstructing under Group Actions." Graphs and Combinatorics 22, no. 3 (2006): 399–419. http://dx.doi.org/10.1007/s00373-006-0675-y.

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40

Babson, Eric, and Dmitry N. Kozlov. "Group actions on posets." Journal of Algebra 285, no. 2 (2005): 439–50. http://dx.doi.org/10.1016/j.jalgebra.2001.07.002.

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41

Dydak, Jerzy. "Overlays and group actions." Topology and its Applications 207 (July 2016): 22–32. http://dx.doi.org/10.1016/j.topol.2016.03.031.

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42

Puppe, V. "Group Actions and Codes." Canadian Journal of Mathematics 53, no. 1 (2001): 212–24. http://dx.doi.org/10.4153/cjm-2001-009-0.

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AbstractA 2-action with “maximal number of isolated fixed points” (i.e., with only isolated fixed points such that dimk(⊕iHi (M; k)) = |M2|, k = ) on a 3-dimensional, closed manifold determines a binary self-dual code of length = . In turn this code determines the cohomology algebra H*(M; k) and the equivariant cohomology . Hence, from results on binary self-dual codes one gets information about the cohomology type of 3-manifolds which admit involutions with maximal number of isolated fixed points. In particular, “most” cohomology types of closed 3-manifolds do not admit such involutions. Gene

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43

Hoshi, Akinari, and Ming-chang Kang. "Twisted symmetric group actions." Pacific Journal of Mathematics 248, no. 2 (2010): 285–304. http://dx.doi.org/10.2140/pjm.2010.248.285.

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44

Isaacs, I. M. "Group actions and orbits." Archiv der Mathematik 98, no. 5 (2012): 399–401. http://dx.doi.org/10.1007/s00013-012-0364-4.

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45

Delucchi, Emanuele, and Sonja Riedel. "Group actions on semimatroids." Advances in Applied Mathematics 95 (April 2018): 199–270. http://dx.doi.org/10.1016/j.aam.2017.11.001.

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46

Derksen, Harm, and Frank Kutzschebauch. "Nonlinearizable holomorphic group actions." Mathematische Annalen 311, no. 1 (1998): 41–53. http://dx.doi.org/10.1007/s002080050175.

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47

Fauntleroy, Amassa. "Unipotent group actions: corrections." Journal of Pure and Applied Algebra 50, no. 2 (1988): 209–10. http://dx.doi.org/10.1016/0022-4049(88)90116-8.

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48

Nowak, Piotr W. "Isoperimetry of group actions." Advances in Mathematics 219, no. 1 (2008): 1–26. http://dx.doi.org/10.1016/j.aim.2008.04.012.

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49

Re, Riccardo. "Supersingularity from group actions." Mathematische Nachrichten 281, no. 4 (2008): 575–81. http://dx.doi.org/10.1002/mana.200510626.

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50

T. Venkatesh, Et al. "Group Actions on Manifolds." Communications on Applied Nonlinear Analysis 31, no. 1 (2024): 136–40. http://dx.doi.org/10.52783/cana.v31.357.

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In this paper some Riemann Geometry aspects will be gathered with classical time, the study naturally concentrate to PDE’s from the relation outside geometry. The classical frame work of differential geometry (intending smooth manifolds) and later it endured with Riemannian metric is briefly described in one of the sections that were formed to be essential for our understanding of the inner structure of the space.

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