On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

Title:

On non-periodic groups whose finitely generated subgroups are either permutable or pronormal

Creator:

Kurdachenko, L. A., Subbotin, I. Ya., and Ermolkevich, T. I.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6c5a5465-4c87-44fd-82d6-52beba5928eb
uuid:6c5a5465-4c87-44fd-82d6-52beba5928eb
doi:10.21136/MB.2013.143230

Subject:

pronormal subgroup, permutable subgroup, finitely generated subgroup, and abnormal subgroup

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The current article considers some infinite groups whose finitely generated subgroups are either permutable or pronormal. A group G is called a generalized radical, if G has an ascending series whose factors are locally nilpotent or locally finite. The class of locally generalized radical groups is quite wide. For instance, it includes all locally finite, locally soluble, and almost locally soluble groups. The main result of this paper is the following Theorem. Let G be a locally generalized radical group whose finitely generated subgroups are either pronormal or permutable. If G is non-periodic then every subgroup of G is permutable.

Language:

English

Rights:

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

Coverage:

61-74

Source:

Mathematica bohemica | 2013 Volume:138 | Number:1

Harvested from:

CDK

Metadata only:

false