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Groups with Subnormal Deviation

Author

Listed:
  • Francesco de Giovanni

    (Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80138 Napoli, Italy
    These authors are supported by GNSAGA (INdAM) and are members of AGTA—Advances in Group Theory and Applications ( www.advgrouptheory.com (accessed on 12 June 2015)).)

  • 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
    These authors are supported by GNSAGA (INdAM) and are members of AGTA—Advances in Group Theory and Applications ( www.advgrouptheory.com (accessed on 12 June 2015)).)

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.

Suggested Citation

  • Francesco de Giovanni & Leonid A. Kurdachenko & Alessio Russo, 2023. "Groups with Subnormal Deviation," Mathematics, MDPI, vol. 11(12), pages 1-7, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2635-:d:1167364
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