Groups with Subnormal Deviation

Francesco de Giovanni (), Leonid A. Kurdachenko and Alessio Russo
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Francesco de Giovanni: Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80138 Napoli, Italy
Leonid A. Kurdachenko: Department of Algebra, National University of Dnipro, 49000 Dnipro, Ukraine
Alessio Russo: Dipartimento di Matematica e Fisica, Università della Campania Luigi Vanvitelli, Via Vivaldi, 81100 Caserta, Italy

Mathematics, 2023, vol. 11, issue 12, 1-7

Abstract: The structure of groups which are rich in subnormal subgroups has been investigated by several authors. Here, we prove that if a periodic soluble group G has subnormal deviation, which means that the set of its non-subnormal subgroups satisfies a very weak chain condition, then either G is a Černikov group or all its subgroups are subnormal. It follows that if a periodic soluble group has a subnormal deviation, then its subnormal deviation is 0.

Keywords: subnormal subgroup; subnormal deviation; minimal condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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