Title: On subnormality criteria for subgroups in finite groups
Abstract: Journal of the London Mathematical SocietyVolume 76, Issue 1 p. 237-252 Articles On subnormality criteria for subgroups in finite groups Francesco Fumagalli, Corresponding Author Francesco Fumagalli [email protected] Dipartimento di Matematica 'Ulisse Dini', Università degli Studi di Firenze, viale Morgagni 67A, 50134 Firenze, [email protected] for more papers by this author Francesco Fumagalli, Corresponding Author Francesco Fumagalli [email protected] Dipartimento di Matematica 'Ulisse Dini', Università degli Studi di Firenze, viale Morgagni 67A, 50134 Firenze, [email protected] for more papers by this author First published: 24 September 2007 https://doi.org/10.1112/jlms/jdm050Citations: 1 2000 Mathematics Subject Classification 20D35. This work was partially supported by the MURST research program 'Teoria dei gruppi e applicazioni'. AboutPDF 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 onFacebookTwitterLinked InRedditWechat Abstract Let H be a subgroup of a finite group G and let S G 1 ( H ) be the set of all elements g of G such that H is subnormal in 〈H, Hg〉. A result of Wielandt states that H is subnormal in G if and only if G = S G 1 ( H ). In this paper, we let A be a subgroup of G contained in S G 1 ( H ) and ask if this implies (and therefore is equivalent to) the subnormality of H in 〈H, A〉. We show with an example that the answer is no, even for soluble groups with Sylow subgroups of nilpotency class at most 2. However, we prove that the two conditions are equivalent whenever A either is subnormal in G or has p-power index in G (for p any prime number). Citing Literature Volume76, Issue1August 2007Pages 237-252 RelatedInformation
Publication Year: 2007
Publication Date: 2007-08-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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