Groups in which every non-nilpotent subgroup is self-normalizing

Costantino Delizia, Urban Jezernik, Primož Moravec, Chiara Nicotera

Abstract


We study the class of groups having the property that every non-nilpotent subgroup is equal to its normalizer. These groups are either soluble or perfect. We describe soluble groups and finite perfect groups with the above property. Furthermore, we give some structural information in the infinite perfect case.

Keywords


Normalizer, non-nilpotent subgroup, self-normalizing subgroup

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DOI: https://doi.org/10.26493/1855-3974.1439.fdf

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications