A NOTE ON COVER-AVOIDING PROPERTIES OF FINITE GROUPS

Abstract

A subgroup H of a group G is said to be a CAP∗-subgroup of a group

G if, for any non-Frattini chief factor K/L of G, we have HK = HL or

H ∩ K = H ∩ L. In this paper, some new characterizations for finite

groups are obtained based on the assumption that some subgroups are

CAP∗-subgroups of G.