Classes of finite groups with generalized subnormal cyclic primary subgroups

We study the properties of the classes ν π ℌ ( ν π * ℌ) of finite groups whose all cyclic primary π-subgroups are ℌ-subnormal (respectively, K-ℌ-subnormal) for a set of primes π and a hereditary homomorph ℌ. It is established that is a hereditary saturated formation if is a hereditary saturated form...

Full description

Saved in:
Bibliographic Details
Published inSiberian mathematical journal Vol. 55; no. 6; pp. 1105 - 1115
Main Author Murashka, V. I.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.11.2014
Subjects
Mathematics
Mathematics and Statistics
finite group
K
homomorph
cyclic primary π-subgroup
subnormal subgroup
hereditary saturated formation
Online AccessGet full text

Cover

More Information
Summary:We study the properties of the classes ν π ℌ ( ν π * ℌ) of finite groups whose all cyclic primary π-subgroups are ℌ-subnormal (respectively, K-ℌ-subnormal) for a set of primes π and a hereditary homomorph ℌ. It is established that is a hereditary saturated formation if is a hereditary saturated formation. We in particular obtain some new criteria for the p -nilpotency and ϕ -dispersivity of finite groups. A characterization of formations with Shemetkov property is obtained in the class of all finite soluble groups.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446614060135