Results 1 to 10 of about 34,720 (216)
On the automorphism groups of relatively free groups of infinite rank: a survey [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2018 The paper is intended to be a survey on some topics within the framework of automorphisms of a relatively free groups of infinite rank. We discuss such properties as tameness, primitivity, small index, Bergman property, and so on.
V.A. Roman’kov
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Automorphisms groups of simplicial complexes of infinite type surfaces [PDF]
Publicacions Matemàtiques, 2016 Let S be an orientable surface of innite genus with a nite numberof boundary components. In this work we consider the curve complex C(S), the nonseparating curve complex N(S), and the Schmutz graph G(S) of S.
Jesús Hernández Hernández +1 more
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A note on fixed points of automorphisms of infinite groups [PDF]
International Journal of Group Theory, 2014 Motivated by a celebrated theorem of Schur, we show that if $Gamma$ is a normal subgroup of the full automorphism group $Aut(G)$ of a group $G$ such that $Inn(G)$ is contained in $Gamma$ and $Aut(G)/Gamma$ has no uncountable abelian subgroups of prime ...
Francesco de Giovanni +2 more
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Acylindrical hyperbolicity of automorphism groups of infinitely-ended groups [PDF]
Journal of Topology, 2020 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 ...
Anthony Genevois, Camille Horbez
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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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Finite groups of automorphisms of infinite groups II
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.
T. Fournelle
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Cayley graphs with few automorphisms: the case of infinite groups [PDF]
Annales Henri Lebesgue, 2020 We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques.
Paul-Henry Leemann, Mikael de la Salle
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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 Rk, Waldemar Hołubowski
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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
R. Cohen
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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
Vladimir Tolstykh
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