Results 1 to 10 of about 248 (23)
Class-preserving Coleman automorphisms of some classes of finite groups
Open Mathematics, 2022 The normalizer problem of integral group rings has been studied extensively in recent years due to its connection with the longstanding isomorphism problem of integral group rings.
Hai Jingjing, Li Zhengxing, Ling Xian
doaj +1 more source
Calculating the virtual cohomological dimension of the automorphism group of a RAAG
Bulletin of the London Mathematical Society, Volume 53, Issue 1, Page 259-273, February 2021., 2021 Abstract We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right‐angled Artin group. The algorithm works in the relative setting; in particular, it also applies to untwisted automorphism groups and basis‐conjugating automorphism groups.
Matthew B. Day +2 more
wiley +1 more source
Homotopy type of the complex of free factors of a free group
Proceedings of the London Mathematical Society, Volume 121, Issue 6, Page 1737-1765, December 2020., 2020 Abstract We show that the complex of free factors of a free group of rank n⩾2 is homotopy equivalent to a wedge of spheres of dimension n−2. We also prove that for n⩾2, the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (n−2)‐connected.
Benjamin Brück, Radhika Gupta
wiley +1 more source
$p$-Groups for which each outer $p$-automorphism centralizes only $p$ elements [PDF]
, 2013 An automorphism of a group is called outer if it is not an inner automorphism. Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\phi$ of $G$ the subgroup $C_G(\phi)=\{x\in G \;|\; x^\phi=x\}$ has order $p$ if and only if $G$ is of ...
Abdollahi, Alireza, Ghoraishi, S. Mohsen
core +3 more sources
Twisted Conjugacy Classes in Lattices in Semisimple Lie Groups [PDF]
, 2012 Given a group automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-conjugacy classes. One says that $\Gamma$ has the $R_\infty$
A Borel +21 more
core +1 more source
Centralizers of automorphisms permuting free generators
Open Mathematics, 2019 By σ ∈ Skm we denote a permutation of the cycle-type km and also the induced automorphism permuting subscripts of free generators in the free group Fkm.
Macedońska Olga, Tomaszewski Witold
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On minimal artinian modules and minimal artinian linear groups
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 12, Page 707-714, 2001., 2001 The paper is devoted to the study of some important types of minimal artinian linear groups. The authors prove that in such classes of groups as hypercentral groups (so also, nilpotent and abelian groups) and FC‐groups, minimal artinian linear groups have precisely the same structure as the corresponding irreducible linear groups.
Leonid A. Kurdachenko, Igor Ya. Subbotin
wiley +1 more source
Free group automorphisms with many fixed points at infinity [PDF]
, 2008 A concrete family of automorphisms alpha_n of the free group F_n is exhibited, for any n > 2, and the following properties are proved: alpha_n is irreducible with irreducible powers, has trivial fixed subgroup, and has 2n-1 attractive as well as 2n ...
Jaeger, Andre, Lustig, Martin
core +2 more sources
Automorphisms fixing every normal subgroup of a nilpotent-by-abelian group
, 2007 Among other things, we prove that the group of automorphisms fixing every normal subgroup of a nilpotent-by-abelian group is nilpotent-by-metabelian. In particular, the group of automorphisms fixing every normal subgroup of a metabelian group is soluble ...
Endimioni, G.
core +1 more source
Fixed points of endomorphisms of graph groups
, 2012 It is shown, for a given graph group $G$, that the fixed point subgroup Fix$\,\varphi$ is finitely generated for every endomorphism $\varphi$ of $G$ if and only if $G$ is a free product of free abelian groups. The same conditions hold for the subgroup of
Rodaro, Emanuele +2 more
core +1 more source