Results 141 to 150 of about 1,094 (186)

Twisting of Graded Quantum Groups and Solutions to the Quantum Yang-Baxter Equation. [PDF]

open access: yesTransform Groups
Huang H   +5 more
europepmc   +1 more source

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

IMPRIMITIVE AUTOMORPHISM GROUPS

The Quarterly Journal of Mathematics, 1992
Let \(G\) be a permutation group on a countably infinite set \(\Omega\), and for every positive integer \(k\) let \(n_ k\) denote the number of orbits under the action of \(G\) on subsets of order \(k\) of \(\Omega\). It was proved by \textit{P. J. Cameron} [Math. Z. 148, 127-139 (1976; Zbl 0313.20022)] that the sequence \((n_ k)_{k\in \mathbb{N}}\) is
openaire   +1 more source

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

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