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Engel-4 Groups of Exponent 5

1997; Wiley; Volume: 74; Issue: 2 Linguagem: Inglês

10.1112/s0024611597000117

1460-244X

Michael Vaughan-Lee,

Finite Group Theory Research

Proceedings of the London Mathematical SocietyVolume 74, Issue 2 p. 306-334 Articles Engel-4 Groups of Exponent 5 M Vaughan-Lee, M Vaughan-Lee [email protected] Christ Church, Oxford, OX1 1DP UKSearch for more papers by this author M Vaughan-Lee, M Vaughan-Lee [email protected] Christ Church, Oxford, OX1 1DP UKSearch for more papers by this author First published: 23 December 2016 https://doi.org/10.1112/S0024611597000117Citations: 14AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract We show that if G is a group of exponent 5, and if G satisfies the Engel-4 identity [x,y,y,y,y]=1, then G is locally finite. By a result of Traustason, this implies that Engel-4 5-groups are locally finite. We also show that a group of exponent 5 is locally finite if and only if it satsifies the identity [ x , [ y , z , z , z , z ] , [ y , z , z , z , z ] ] = 1. This result implies that a group of exponent 5 is locally finite if its three generator subgroups are finite. 1991 Mathematics Subject Classification: 20D15, 20F45, 20F50. Citing Literature Volume74, Issue2March 1997Pages 306-334 RelatedInformation