Abstract
Let G be a finite group. A subgroup H of G is called a BNA-subgroup of G if either or
for all
A subgroup H of G is said to be a weakly BNA-subgroup of G if there exists a normal subgroup T of G such that G = HT and
is a BNA-subgroup of G. In this paper, we investigate the solvability, supersolvability, and p-nilpotency of a finite group G under the assumption that certain minimal subgroups and cyclic subgroups of order 4 are weakly BNA-subgroups of G.
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