Answer to a 1962 question by Zappa on cosets of Sylow subgroups

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dc.contributor.author Conder, Marston en
dc.date.accessioned 2018-10-10T23:14:25Z en
dc.date.issued 2017-06-20 en
dc.identifier.citation Advances in Mathematics 313:167-175 20 Jun 2017 en
dc.identifier.issn 0001-8708 en
dc.identifier.uri http://hdl.handle.net/2292/40621 en
dc.description.abstract In a paper in 1962, Guido Zappa asked whether a non-trivial coset of a Sylow p-subgroup of a finite group could contain only elements whose orders are powers of p, and also in that case, at least one element of order p. The first question was raised again recently in a 2014 paper by Daniel Goldstein and Robert Guralnick, when generalising an answer by John Thompson in 1967 to a similar question by L.J. Paige. In this paper we give a positive answer to both questions of Zappa, showing somewhat surprisingly that in a number of non-abelian finite simple groups (including PSL(3,4), PSU(5,2) and the Janko group J3), some non-trivial coset of a Sylow 5-subgroup (of order 5) contains only elements of order 5. Also Zappa's first question is studied in more detail. Various possibilities for the group and its Sylow p-subgroup P are eliminated, and it then follows that |P|≥5 and |P|≠8. It is an open question as to whether the order of the Sylow p-subgroup can be 7 or 9 or more. en
dc.language English en
dc.publisher Elsevier en
dc.relation.ispartofseries Advances in Mathematics en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.rights.uri https://www.elsevier.com/journals/advances-in-mathematics/0001-8708/guide-for-authors#13300 en
dc.subject Science & Technology en
dc.subject Physical Sciences en
dc.subject Mathematics en
dc.subject Finite group en
dc.subject Sylow subgroup en
dc.subject Element orders en
dc.subject FINITE GROUPS en
dc.subject P-SUBGROUP en
dc.subject CRITERION en
dc.subject ELEMENT en
dc.subject BELONG en
dc.title Answer to a 1962 question by Zappa on cosets of Sylow subgroups en
dc.type Journal Article en
dc.identifier.doi 10.1016/j.aim.2017.04.011 en
pubs.begin-page 167 en
pubs.volume 313 en
dc.rights.holder Copyright: Elsevier en
pubs.author-url http://www.sciencedirect.com/science/article/pii/S0001870816315778 en
pubs.end-page 175 en
pubs.publication-status Published en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.subtype Article en
pubs.elements-id 624458 en
pubs.org-id Science en
pubs.org-id Mathematics en
dc.identifier.eissn 1090-2082 en
pubs.record-created-at-source-date 2019-07-08 en
pubs.online-publication-date 2017-05-16 en


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