JP Journal of Algebra, Number Theory and Applications
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Abstract: A
subgroup H of G is called a PCM-subgroup (or H
is PCM in G) if H is permutable with at least one conjugate of each maximal subgroup
of G, that is, for any maximal subgroup M
of G, there exists an element such that The aim of this paper is to
investigate the structure of a finite group under the assumption that certain
subgroups are PCM-subgroups, and obtain some sufficient andnecessary conditions for supersolvability.
Keywords and phrases: PCM-subgroup, supersolvable group, solvable group, formation.
