Hall classes in linear groups

Author:

de Giovanni Francesco1,Trombetti Marco1ORCID,Wehrfritz Bertram A. F.2

Affiliation:

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

2. School of Mathematical Sciences , Queen Mary University of London , London , United Kingdom

Abstract

Abstract A well-known theorem of Philip Hall states that if a group 𝐺 has a nilpotent normal subgroup 𝑁 such that G / N G/N^{\prime} is nilpotent, then 𝐺 itself is nilpotent. We say that a group class 𝔛 is a Hall class if it contains every group 𝐺 admitting a nilpotent normal subgroup 𝑁 such that G / N G/N^{\prime} belongs to 𝔛. Examples have been given in [F. de Giovanni, M. Trombetti and B. A. F. Wehfritz, Hall classes of groups, to appear] to show that finite-by-𝔛 groups do not form a Hall class for many natural choices of the Hall class 𝔛. Although these examples are often linear, our aim here is to prove that the situation is much better within certain natural subclasses of the universe of linear groups.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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. Hall classes of groups;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2024-01-18

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