<abstract xmlns="http://www.w3.org/1999/xhtml">

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

Action of Aut(<italic>G</italic>) on the set of maximal subgroups of <italic>p</italic>-groups

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

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...

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

Published Online: Sep 05, 2022

Page range: 2451 - 2458

Received: Jan 25, 2022

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/amns.2022.1.00023

Keywords
AMS 2010 codes:

© 2023 Sun Xiu-juan, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Sep 05, 2022

Page range: 2451 - 2458

Received: Jan 25, 2022

Accepted: May 15, 2022

DOI: https://doi.org/10.2478/amns.2022.1.00023

KeywordsAMS 2010 codes:

© 2023 Sun Xiu-juan, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
AMS 2010 codes: