Action of Aut(<i>G</i>) on the set of maximal subgroups of <i>p</i>-groups-Reference-Cited by-同舟云学术

Action of Aut(G) on the set of maximal subgroups of p-groups

Published:2022-09-05 Issue:0 Volume:0 Page:
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Xiu-juan Sun¹,Mohamed Hamdy²

Affiliation:

1. School of Mathematics and Computational Sciences , Tangshan Teachers College , Tangshan , Hebei , China

2. College of Engineering , Applied Science University , Al Eker , Bahrain

Abstract

Abstract In this paper, we mainly study the action of Aut(G) on the set Ω of all maximal subgroups of G, and we use P to denote the action of Aut(G) on Ω. When G is a finite non-cyclic abelian p-group, P is transitive. When G is minimal non-abelian, there are three cases. If G is quaternion group, P is transitive; if G is a metacyclic group, P is non-transitive; if G is not a metacyclic group, P is transitive.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.2478/amns.2022.1.00023

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