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On conormal subgroups

Published:2022-02-17 Issue:02 Volume:32 Page:327-345
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

Dixon Martyn R.¹,Kurdachenko Leonid A.²,Subbotin Igor Ya.³

Affiliation:

1. Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA

2. Department of Algebra, Facultet of Mathematic and Mechanik, National University of Dnepropetrovsk, Gagarin Prospect 72, Dnipro 10, 49010, Ukraine

3. Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, Los Angeles, CA 90045-6904, USA

Abstract

We introduce the concept of a conormal subgroup: a subgroup is conormal if it is contranormal in its normal closure. This unifies the concepts of normal and contranormal subgroups. We obtain some important properties of conormal subgroups, describe their connections with transitivity of normality, and study groups in which all conormal subgroups are normal.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196722500163

Reference34 articles.

1. Nilpotent self-normalizing subgroups of soluble groups

2. On the structure of some contranormal-free groups

3. A note on subnormal and abnormal chains

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. ON SOME GROUPS WHOSE SUBNORMAL SUBGROUPS ARE CONTRANORMAL-FREE;INT J GROUP THEORY;2025

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