Infinite groups of finite period.
type: Item
instance of: scholarly article
title: Infinite groups of finite period.
zbMATH Open document ID: 1332.20042
author: N. E. Zubov
published in: Algebra and Logic
publication date: 2015-10-27T00:00:00Z
review text: A first, important, result of this paper is that there exist periodic groups containing elements of even order and only trivial normal \(2\)-subgroups, in which every pair of involutions generates a \(2\)-group. This proves that, in general, the Baer-Suzuki theorem cannot be extended to periodic groups and gives a negative answer to Question 11.11a in the \textit{Kourovka Notebook} [1990; Zbl 0748.20001]. As a consequence the authors point out examples of finite simple groups that are recognizable by spectrum in the class of finite groups but are not recognizable in the class of all groups. Reviewer's remark: In the English translation ``Baer-Suzuki theorem'' has become ``Baire-Suzuki theorem''.
reviewed by: Enrico Jabara
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 6498559
zbMATH Keywords: periodic groups
zbMATH Keywords: periodic products
zbMATH Keywords: spectra of groups
zbMATH Keywords: recognizability by spectrum
zbMATH Keywords: Baer-Suzuki theorem
zbMATH Keywords: finite simple groups
zbMATH Keywords: modular group
MaRDI profile type: Publication
full work available at URL: s10469-015-9335-8
OpenAlex ID: W2287157488
cites work: The Kourovka notebook. Unsolved problems in group theory.
cites work: Periodic products of groups
cites work: THE FREE BURNSIDE GROUPS OF SUFFICIENTLY LARGE EXPONENTS
cites work: On recognizing the finite simple groups \(L_2(2^m)\) in the class of all groups
cites work: Recognizability by spectrum of the group \(L_2(7)\) in the class of all groups.
cites work: Recognizing \(L_3(4)\) by the set of element orders in the class of all groups.
cites work: The characterization of \(\text{PSL}(2,q)\) by its element orders
cites work: Some groups of exponent \(72\).
DOI: 10.1007/S10469-015-9335-8
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description: scientific article; zbMATH DE number 6498559