Results 1 to 10 of about 250 (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, Andrew W. Sale, Richard D. Wade   +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, A Fel’shtyn, A Fel’shtyn, A Fel’shtyn, A Fel’shtyn, A Fel’shtyn, C Bleak, DL Gonçalves, DL Gonçalves, G Hochschild, G Levitt, G Levitt, GD Mostow, J Millson, MS Raghunathan, P Deligne, P. SANKARAN, R Lyndon, RJ Zimmer, S Helgason, T. MUBEENA, V Roman’kov   +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
doaj   +1 more source

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

Groups not presentable by products [PDF]

, 2011
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and certain geometric ...
Kotschick, D., Loeh, C.
core   +3 more sources

Extension and reconstruction theorems for the Urysohn universal metric space [PDF]

, 2009
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.Comment: Final and shortened version,
A. H. Mekler, A. M. Vershik, J. D. Clemens, J. E. Baumgartner, J. E. Baumgartner, M. Džamonja, M. Džamonja, M. Gromov, M. Hrusak, M. Kojman, M. Kojman, M. Kojman, M. Kojman, Menachem Kojman, S. Shelah, S. Shelah, S. Shelah, S. Shelah, Saharon Shelah, W. H. Woodin   +19 more
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