Abstract
AbstractA subgroup H of a group G is said to be Frattini closed in G if either $$H=G$$
H
=
G
or H is the intersection of all maximal subgroups of G containing H. The structure of a soluble group in which every subgroup is Frattini closed is known. In this paper, the behavior of a (generalized) soluble group G in which every subgroup is Frattini closed in a subgroup of finite index of G is studied. Among other results, it is proved that if G is a (generalized) soluble group and there exists a positive integer k such that every subgroup of G is Frattini closed in a subgroup of index at most k in G, then G contains a normal subgroup of finite index in which all subgroups are Frattini closed.
Funder
Università degli Studi di Napoli Federico II
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
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