Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements

Title:

Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements

Creator:

Shao, Changguo and Jiang, Qinhui

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:175beeba-3a1b-4802-96ba-42979c1f0589
uuid:175beeba-3a1b-4802-96ba-42979c1f0589

Subject:

finite group and number of subgroups of possible orders

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups $G$ whose set of numbers of subgroups of possible orders $n(G)$ has exactly two elements. We show that if $G$ is a non-nilpotent group whose set of numbers of subgroups of possible orders has exactly 2 elements, then $G$ has a normal Sylow subgroup of prime order and $G $ is solvable. Moreover, as an application we give a detailed description of non-nilpotent groups with $n(G)=\{1, q+1\}$ for some prime $q$. In particular, $G$ is supersolvable under this condition.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

827-831

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:3

Harvested from:

CDK

Metadata only:

false