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Relevant bibliographies by topics / Fixed point subgroup

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Academic literature on the topic 'Fixed point subgroup'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Fixed point subgroup"

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Cullinan, John. "Fixed-point subgroups of GL3(𝑞)". Journal of Group Theory 22, № 5 (2019): 893–914. http://dx.doi.org/10.1515/jgth-2018-0160.

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Abstract Let V be a vector space over a field k. We call a subgroup {G\subset\mathrm{GL}(V)} a fixed-point subgroup if {\det(1-g)=0} for all {g\in G} . Let q be a power of a prime. In this paper, we classify the fixed-point subgroups of {\mathrm{GL}_{3}(q)} .

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RIBÓN, JAVIER. "Fixed points of nilpotent actions on." Ergodic Theory and Dynamical Systems 36, no. 1 (2014): 173–97. http://dx.doi.org/10.1017/etds.2014.58.

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We prove that a nilpotent subgroup of orientation-preserving$C^{1}$diffeomorphisms of$\mathbb{S}^{2}$has a finite orbit of cardinality at most two. We also prove that a finitely generated nilpotent subgroup of orientation-preserving$C^{1}$diffeomorphisms of$\mathbb{R}^{2}$preserving a compact set has a global fixed point. These results generalize theorems of Frankset al for the abelian case. We show that a nilpotent subgroup of orientation-preserving$C^{1}$diffeomorphisms of$\mathbb{S}^{2}$that has a finite orbit of odd cardinality also has a global fixed point. Moreover, we study the properti

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Beltr�n, Antonio. "Actions with nilpotent fixed point subgroup." Archiv der Mathematik 69, no. 3 (1997): 177–84. http://dx.doi.org/10.1007/s000130050107.

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Beltrán, Antonio, and Changguo Shao. "Conditions for Sylow 2-subgroups of the Fixed Point Subgroup Implying Solubility." Proceedings of the Edinburgh Mathematical Society 62, no. 1 (2018): 211–20. http://dx.doi.org/10.1017/s0013091518000251.

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AbstractLet A and G be finite groups and suppose that A acts via automorphisms on G with $(|A|, |G|)=1$. We study how certain conditions on the Sylow 2-subgroups of the fixed point subgroup of the action $C_G(A)$ may imply the non-simplicity or solubility of G.

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Türkan, Erkan Murat. "Implications of the index of a fixed point subgroup." Rendiconti del Seminario Matematico della Università di Padova 142 (June 11, 2019): 1–7. http://dx.doi.org/10.4171/rsmup/26.

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Jiang, Qinhui, Zhaoying Chen, and Kefeng Li. "Sylow 2-subgroups of the fixed point subgroup and the solvability of finite groups." Journal of Algebra and Its Applications 18, no. 04 (2019): 1950080. http://dx.doi.org/10.1142/s0219498819500804.

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Let [Formula: see text] be a finite group which acts coprimely on finite group [Formula: see text] via automorphisms. We investigate the influence of the structural conditions of the Sylow [Formula: see text]-subgroups of the fixed point subgroup of the action, [Formula: see text], working on the non-simplicity or solvability of [Formula: see text].

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Khukhro, E. I., N. Yu Makarenko, and P. Shumyatsky. "Finite Groups and Lie Rings with an Automorphism of Order 2n." Proceedings of the Edinburgh Mathematical Society 60, no. 2 (2016): 391–412. http://dx.doi.org/10.1017/s0013091516000225.

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AbstractSuppose that a finite groupGadmits an automorphismof order 2nsuch that the fixed-point subgroupof the involutionis nilpotent of classc. Letm=) be the number of fixed points of. It is proved thatGhas a characteristic soluble subgroup of derived length bounded in terms ofn,cwhose index is bounded in terms ofm,n,c. A similar result is also proved for Lie rings.

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GÜLOĞLU, İSMAİL Ş., and GÜLİN ERCAN. "A GENERALIZED FIXED-POINT-FREE ACTION." Journal of Algebra and Its Applications 12, no. 03 (2012): 1250172. http://dx.doi.org/10.1142/s0219498812501721.

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In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x ∈ CG(A) of prime order or of order 4, every conjugate of x in G is also contained in CG(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.

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FRANKS, JOHN, MICHAEL HANDEL, and KAMLESH PARWANI. "Fixed points of abelian actions on S2." Ergodic Theory and Dynamical Systems 27, no. 5 (2007): 1557–81. http://dx.doi.org/10.1017/s0143385706001088.

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AbstractWe prove that if ${\mathcal F}$ is a finitely generated abelian group of orientation preserving C1 diffeomorphisms of $\mathbb {R}^2$ which leaves invariant a compact set then there is a common fixed point for all elements of ${\mathcal F}$. We also show that if ${\mathcal F}$ is any abelian subgroup of orientation preserving C1 diffeomorphisms of S2 then there is a common fixed point for all elements of a subgroup of ${\mathcal F}$ with index at most two.

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Jabara, Enrico. "Fixed Point Free Actions of Groups of Exponent 5." Journal of the Australian Mathematical Society 77, no. 3 (2004): 297–304. http://dx.doi.org/10.1017/s1446788700014440.

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AbstractIn this paper we prove that if V is a vector space over a field of positive characteristric p ≠ 5 then any regular subgroup A of exponent 5 of GL(V) is cyclic. As a consequence a conjecture of Gupta and Mazurov is proved to be true.

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Dissertations / Theses on the topic "Fixed point subgroup"

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Turkan, Erkan Murat. "On The Index Of Fixed Point Subgroup." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613522/index.pdf.

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Let G be a finite group and A be a subgroup of Aut(G). In this work, we studied the influence of the index of fixed point subgroup of A in G on the structure of G. When A is cyclic, we proved the following: (1) [G,A] is solvable if this index is squarefree and the orders of G and A are coprime. (2) G is solvable if the index of the centralizer of each x in H-G is squarefree where H denotes the semidirect product of G by A. Moreover, for an arbitrary subgroup A of Aut(G) whose order is coprime to the order of G, we showed that when G is solvable, then the Fitting length f([G,A]) of [G,A] is

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Books on the topic "Fixed point subgroup"

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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Fixed Point Buildings. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0022.

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This chapter presents the proof for the Fundamental Theorem of Descent in buildings: that if Γ‎ is a descent group, the set of residues of a building Δ‎ that are stabilized by a subgroup Γ‎ of Aut(Γ‎) forms a thick building. It begins with the hypothesis: Let Π‎ be an arbitrary Coxeter diagram, let S be the vertex set of Π‎ and let (W, S) be the corresponding Coxeter system. It then defines a Γ‎-residue and a Γ‎-chamber as well as a descent group of Δ‎ before concluding with the main result about the fixed point building of Γ‎.

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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Unramified Galois Involutions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0032.

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This chapter describes the fixed point building of an automorphism of a Bruhat-Tits building Ξ‎ which induces an unramified Galois involution on the building at infinity Ξ‎∞. An element of G (for example, a Galois involution of Δ‎) is unramified if the subgroup of G it generates is unramified. Before presenting the main result, the chapter presents the notation stating that Δ‎ = Ξ‎∞ is the building at infinity of Ξ‎ with respect to its complete system of apartments and G = Aut(Δ‎), followed by definitions. The central theorem shows how an unramified Galois involution of Δ‎ is obtained. Here Γ‎

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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Moufang Structures. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0024.

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This chapter uses the notion of a Moufang structure to show that if Δ‎ is a spherical building satisfying the Moufang condition and Γ‎ is a descent group of Δ‎, then the fixed point building Δ‎Γ‎ also satisfies the Moufang condition. The discussion begins with the notation: Let (W, S) denote the type of Δ‎, let G = Aut(Δ‎) and let G° denote the group of type-preserving elements of G. The chapter then presents the conditions for an element g of G to be unipotent and for a subgroup U of G to be unipotent. It also describes a unipotent group U stabilizing a residue R and a unipotent element fixin

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Book chapters on the topic "Fixed point subgroup"

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Bogopolski, Oleg, and Olga Maslakova. "An Efficient Algorithm for Finding a Basis of the Fixed Point Subgroup of an Automorphism of a Free Group." In Trends in Mathematics. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05488-9_3.

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Leite, Jorge, Munir Boodhwani, and Felipe Fregni. "Other Issues in Statistics II." In Critical Thinking in Clinical Research, edited by Claudia Kimie Suemoto, Catherine Lee, and Felipe Fregni. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199324491.003.0014.

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This chapter focuses on two important concepts: subgroup analysis and meta-analysis. Subgroup analysis is especially concerned about variability and how treatment effects can differ due to specific characteristics of the population. Important issues, however, arise when planning for subgroup analysis, such as dealing with false positives and methods for dealing with multiple statistical comparisons. The chapter also points out that the analysis of data from subgroups of patients with certain baseline characteristics is typically insufficient to change general clinical practice. The second section of this chapter focuses on meta-analysis, which is a method of pooling data from several studies in order to quantify the overall effect of an intervention or exposure, and thus potentially change clinical practice. This section discusses data search and synthesis, quantification of heterogeneity, choice of fixed or random model, as well as sensitivity analysis.

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Conference papers on the topic "Fixed point subgroup"

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NAVARRO, G. "FIXED POINT SUBGROUPS AND CHARACTER TABLES." In Proceedings of the Conference. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814350051_0021.

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Guay, Franc¸ois, Jean-Franc¸ois Collard, Philippe Cardou, and Marc Gouttefarde. "An Improved Branch-and-Bound Algorithm for Minimizing the Potential Energy of a Cable-Suspended Rigid Body." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48169.

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We compute the lowest stable-equilibrium pose of a rigid body suspended in space by an arbitrary number of cables, being given the cable lengths and the attachment-point positions on the fixed frame and on the rigid body. This fundamental problem of mechanics if of interest in the fields of underconstrained cable-driven parallel robots and cooperative towing. The approach of the present work is very similar to one that is reported in a previous paper by the authors. Indeed, the problem is formulated as a potential energy minimization, and is solved using a branch-and-bound algorithm. Hence, we

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