Groups in which every non-abelian subgroup is self-normalized

Costantino Delizia; Urban Jezernik; Primoz Moravec; Chiara Nicotera

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arXiv · 1607.07366

Groups in which every non-abelian subgroup is self-normalized

Costantino Delizia·Urban Jezernik·Primoz Moravec·Chiara Nicotera

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Abstract

We study groups having the property that every non-abelian subgroup is equal to its normalizer. This class of groups is closely related to an open problem posed by Berkovich. We give a full classification of finite groups having the above property. We also describe all infinite soluble groups in this class.

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Costantino Delizia, Urban Jezernik, Primoz Moravec, Chiara Nicotera. 2016-07-25. Groups in which every non-abelian subgroup is self-normalized. https://arxiv.org/abs/1607.07366

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