Results 151 to 160 of about 735 (188)

Automorphisms of Automorphism Group of Dihedral Groups

Creative Mathematics and Informatics, 2023
The automorphism group of a Dihedral group of order 2n is isomorphic to the holomorph of a cyclic group of order n. The holomorph of a cyclic group of order n is a complete group when n is odd. Hence automorphism groups of Dihedral groups of order 2n are its own automorphism groups whenever n is odd. In this paper, we prove that the result is also true
Sajikumar, Sadanandan   +2 more
openaire   +2 more sources

Automorphism Groups of Nilpotent Groups

Bulletin of the London Mathematical Society, 1989
Let \({\mathfrak X}\) denote the class of all finitely generated torsion-free nilpotent groups G such that the derived factor group G/G' is torsion- free. For G in \({\mathfrak X}\), let Aut *(G) denote the group of automorphisms of G/G' induced by the automorphism group of G. If G/G' has rank n and we choose a \({\mathbb{Z}}\)-basis for G/G' then Aut *
Bryant, R. M., Papistas, A.
openaire   +3 more sources

Noetherian Automorphisms of Groups

Mediterranean Journal of Mathematics, 2005
An automorphism α of a group G is called a noetherian automorphism if for each ascending chain $$ X_1 < X_2 < \ldots < X_n < X_{n + 1} < \ldots $$ of subgroups of G there is a positive integer m such that \(X_n^{\alpha} = X_n \) for all n ≥ m. The structure of the group of all noetherian automorphisms of a group is investigated in this paper.
DE GIOVANNI, FRANCESCO, DE MARI, FAUSTO
openaire   +2 more sources

Small Groups of Automorphisms

Bulletin of the London Mathematical Society, 1998
Let \(A\) be a group of automorphisms of the finite group \(G\) such that \((|A|,|G|)=1\). The authors prove that \(|A|0\), groups \(G\) and \(A\leq\Aut(G)\) can be found such that \((|A|,|G|)=1\) and \(|A|>|G|^{2-\varepsilon}\). Furthermore, if \(A\) is nilpotent of class at most 2, then \(|A|
Pálfy, P. P., Pyber, L.
openaire   +1 more source

Automorphism groups of nilpotent groups

Archiv der Mathematik, 2003
\textit{M. Dugas} and \textit{R. Göbel} [Arch. Math. 54, No. 4, 340-351 (1990: Zbl 0703.20033)] proved the following result: if \(H\) is any group, there is a torsion-free nilpotent group \(G\) of class \(2\) such that \(\Aut(G)=H\ltimes\text{Stab}(G)\), where \(\text{Stab}(G)\) is the stability group of the series \(1\triangleleft Z(G)\triangleleft G\)
Braun, Gábor, Göbel, Rüdiger
openaire   +2 more sources

Automorphisms of Metabelian Groups

Canadian Mathematical Bulletin, 1998
AbstractWe investigate the problem of determining when IA(Fn(AmA)) is finitely generated for all n and m, with n ≥ 2 and m ≠ 1. If m is a nonsquare free integer then IA(Fn(AmA)) is not finitely generated for all n and if m is a square free integer then IA(Fn(AmA)) is finitely generated for all n, with n ≠ 3, and IA(F3(AmA)) is not finitely generated ...
openaire   +1 more source

Automorphism groups of metabelian groups

Mathematical Notes of the Academy of Sciences of the USSR, 1987
Translation from Mat. Zametki 41, No.1, 9-22 (Russian) (1987; Zbl 0617.20017).
openaire   +1 more source

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