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Groups all cyclic subgroups of which are BNA-subgroups. (English) Zbl 07030452
Ukr. Math. J. 69, No. 2, 331-336 (2017) and Ukr. Mat. Zh. 69, No. 2, 284-288 (2017).
Summary: 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 $$x\in \langle H,H^x\rangle$$ for all $$x\in G$$. 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.
##### MSC:
 20 Group theory and generalizations 05 Combinatorics
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##### References:
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