{"title":"Generating Sets of Conjugate Involutions of Groups PSLn(9)","authors":"R. I. Gvozdev","doi":"10.1007/s10469-024-09748-z","DOIUrl":null,"url":null,"abstract":"<p>G. Malle, J. Saxl, and T. Weigel in [Geom. Ded., <b>49</b>, No. 1, 85-116 (1994)] formulated the following problem: For every finite simple non-Abelian group <i>G</i>, find the minimum number <i>n</i><sub><i>c</i></sub>(<i>G</i>) of generators of conjugate involutions whose product equals 1. (See also Question 14.69c in [Unsolved Problems in Group Theory. The Kourovka Notebook, No. 20, E. I. Khukhro and V. D. Mazurov (Eds.), Sobolev Institute of Mathematics SO RAN, Novosibirsk (2022); https://alglog.org/20tkt.pdf].) J. M. Ward [PhD Thesis, Queen Mary College, Univ. London (2009)] solved this problem for sporadic, alternating, and projective special linear groups <i>PSL</i><sub><i>n</i></sub>(<i>q</i>) over a field of odd order <i>q</i>, except in the case <i>q</i> = 9 for <i>n</i> ≥ 4 and also in the case <i>q</i> ≡ 3 (mod 4) for <i>n</i> = 6. Here we lift the restriction <i>q</i> ≠ 9 for dimensions <i>n</i> ≥ 9 and <i>n</i> = 6.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-024-09748-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
Abstract
G. Malle, J. Saxl, and T. Weigel in [Geom. Ded., 49, No. 1, 85-116 (1994)] formulated the following problem: For every finite simple non-Abelian group G, find the minimum number nc(G) of generators of conjugate involutions whose product equals 1. (See also Question 14.69c in [Unsolved Problems in Group Theory. The Kourovka Notebook, No. 20, E. I. Khukhro and V. D. Mazurov (Eds.), Sobolev Institute of Mathematics SO RAN, Novosibirsk (2022); https://alglog.org/20tkt.pdf].) J. M. Ward [PhD Thesis, Queen Mary College, Univ. London (2009)] solved this problem for sporadic, alternating, and projective special linear groups PSLn(q) over a field of odd order q, except in the case q = 9 for n ≥ 4 and also in the case q ≡ 3 (mod 4) for n = 6. Here we lift the restriction q ≠ 9 for dimensions n ≥ 9 and n = 6.
期刊介绍：
This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions.
Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences.
All articles are peer-reviewed.
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