Groups with Subnormal Deviation-Reference-Cited by-同舟云学术

Groups with Subnormal Deviation

Published:2023-06-09 Issue:12 Volume:11 Page:2635
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

de Giovanni Francesco¹,Kurdachenko Leonid A.²,Russo Alessio³

Affiliation:

1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80138 Napoli, Italy

2. Department of Algebra, National University of Dnipro, 49000 Dnipro, Ukraine

3. Dipartimento di Matematica e Fisica, Università della Campania Luigi Vanvitelli, Via Vivaldi, 81100 Caserta, Italy

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.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/12/2635/pdf

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4. Franciosi, S., and de Giovanni, F. (1996). Infinite Groups 1994, De Gruyter.

5. Groups with the maximal condition on nonsubnormal subgroups;Kurdachenko;Boll. Un. Mat. Ital.,1996

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