A note on the supersolubility of a group with ms-supersoluble factors

A subgroup A of a group G is called seminormal in G , if there exists a subgroup B such that G = A B and AX  is a subgroup of G for every subgroup X of B . Let G  be a supersoluble group. Then it has an ordered Sylow tower of supersoluble type  1 = G 0 < G 1 < ⋯ < G m = G . If for every  i...

Full description

Saved in:
Bibliographic Details
Published in:Ricerche di matematica 2021-11, Vol.70 (2), p.517-521
Main Author: Trofimuk, Alexander
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
Subgroups
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A subgroup A of a group G is called seminormal in G , if there exists a subgroup B such that G = A B and AX  is a subgroup of G for every subgroup X of B . Let G  be a supersoluble group. Then it has an ordered Sylow tower of supersoluble type  1 = G 0 < G 1 < ⋯ < G m = G . If for every  i all maximal subgroups of  G i / G i - 1 are seminormal in  G / G i - 1 , then  G is said to be ms - supersoluble . In this paper, we proved the supersolubility of a group G = A B under condition that  A and  B are normal in  G and ms -supersoluble.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-020-00493-w