Groups All Cyclic Subgroups of Which are BNA-Subgroups
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Suppose that G is a finite group and H is a subgroup of G. We say that H is a BNA-subgroup of G if either H x = H or x ∈ <H, H x > for all x ∈ G. The BNA-subgroups of G are between normal and abnormal subgroups of G. We obtain some new characterizations for finite groups based on the assumption that all cyclic subgroups are BNA-subgroups.
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