Results 1 to 10 of about 259 (146)
Finite groups of automorphisms of infinite groups, I
Journal of Algebra, 1981 AbstractThis paper studies Aut A in the case in which A is an infinite abelian group and Aut A is finite. Information is obtained about the structure of Aut A including the description of a large normal subgroup. Aut A is completely characterized when it is abelian. Its order is determined when it is dihedral or generalized quaternion.
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Automorphisms of Coxeter Groups of Rank 3 with Infinite Bonds
Journal of Algebra, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Kazhdan groups with infinite outer automorphism group [PDF]
Transactions of the American Mathematical Society, 2006 For each countable group $Q$ we produce a short exact sequence $1\to N \to G \to Q\to 1$ where $G$ is f.g. and has a graphical $\frac16$ presentation and $N$ is f.g. and satisfies property $T$. As a consequence we produce a group $N$ with property $T$ such that $\Out(N)$ is infinite.
Ollivier, Yann, Wise, Daniel T.
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FREE GROUPS AND AUTOMORPHISM GROUPS OF INFINITE STRUCTURES [PDF]
Forum of Mathematics, Sigma, 2014 AbstractGiven a cardinal$\lambda $with$\lambda =\lambda ^{\aleph _0}$, we show that there is a field of cardinality$\lambda $whose automorphism group is a free group of rank$2^\lambda $. In the proof of this statement, we develop general techniques that enable us to realize certain groups as the automorphism group of structures of a given cardinality ...
PHILIPP LÜCKE, SAHARON SHELAH
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Automorphisms of a free group of infinite rank [PDF]
St. Petersburg Mathematical Journal, 2008 The authors study the automorphisms \(\Aut(F_\infty)\) of the free group \(F_\infty\) of infinite countable rank. They describe this group in terms of generators which arise naturally. They use the sets of upper triangular, lower triangular, permutational and column finite automorphisms with the obvious meaning.
Gupta, C. K., Hołubowski, W.
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On groups with a central automorphism of infinite order [PDF]
Proceedings of the American Mathematical Society, 1992 It is shown that a group G G , whose center has finite exponent, has a central automorphism of infinite order if and only ...
Dixon, Martyn R., Evans, M. J.
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Acylindrical hyperbolicity of automorphism groups of infinitely ended groups
Journal of Topology, 2021 We prove that the automorphism group of every infinitely-ended finitely generated group is acylindrically hyperbolic. In particular $\mathrm{Aut}(\mathbb{F}_n)$ is acylindrically hyperbolic for every $n\ge 2$. More generally, if $G$ is a group which is not virtually cyclic, and hyperbolic relative to a finite collection $\mathcal{P}$ of finitely ...
Genevois, Anthony, Horbez, Camille
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The Automorphisms of the Unitary Groups Over Infinite Fields
American Journal of Mathematics, 1973 exaly +3 more sources
The Automorphism Groups of Minimal Infinite Circulant Digraphs
European Journal of Combinatorics, 1997 Given a group \(G\), a directed graph \(X\) is called a digraph regular representation (DRR) of \(G\) if Aut\((X)\simeq G\) (as abstract groups) and the action of Aut\((X)\) on \(V(X)\) is that of a regular permutation group. It is well known that in this case \(X\) must be a Cayley digraph \(X(G,S)\) where \(S\subset G\) and \(\langle S\rangle=G ...
Jixiang Meng, Qiongxiang Huang
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Automorphisms groups of simplicial complexes of infinite type surfaces [PDF]
Publicacions Matemàtiques, 2017 23 pages, 13 ...
Hernández, Jesús Hernández +1 more
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