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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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