Results 1 to 10 of about 249 (146)
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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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 groups of simplicial complexes of infinite type surfaces [PDF]
Publicacions Matemàtiques, 2017 23 pages, 13 ...
Hernández, Jesús Hernández +1 more
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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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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 ...
Meng, Jixiang, Qiongxing, Huang
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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 if G G has an infinite abelian direct factor. It is also shown that the group of central automorphisms of a nilpotent p p -group of infinite exponent contains an uncountable ...
Dixon, Martyn R., Evans, M. J.
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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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Infinite-dimensionality of the automorphism groups of homogeneous Stein manifolds [PDF]
Mathematische Annalen, 2008 We show that the group of holomorphic automorphisms of a Stein manifold X of dimension greater than 1 is infinite-dimensional, provided X is a homogeneous space of a holomorphic action of a complex Lie group.
Huckleberry, Alan, Isaev, Alexander
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Infinitely generated free nilpotent groups: completeness of the automorphism groups [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2009 AbstractWe transfer the results of Dyer, Formanek and Kassabov on the automorphism towers of finitely generated free nilpotent groups to infinitely generated free nilpotent groups. We prove that the automorphism groups of infinitely generated free nilpotent groups are complete. By combining the results of Dyer, Formanek and Kassabov with the results in
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Classes of Automorphisms of Free Groups of Infinite Rank [PDF]
Transactions of the American Mathematical Society, 1973 This paper is concerned with finding classes of automorphisms of an infinitely generated free group F which can be generated by “elementary” Nielsen transformations. Two different notions of “elementary” Nielsen transformations are explored. One leads to a classification of the automorphisms generated by these transformations. The other notion leads to
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