dc.contributor.author |
Conder, Marston |
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dc.date.accessioned |
2018-10-10T23:14:25Z |
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dc.date.issued |
2017-06-20 |
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dc.identifier.citation |
Advances in Mathematics 313:167-175 20 Jun 2017 |
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dc.identifier.issn |
0001-8708 |
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dc.identifier.uri |
http://hdl.handle.net/2292/40621 |
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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. |
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dc.language |
English |
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dc.publisher |
Elsevier |
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dc.relation.ispartofseries |
Advances in Mathematics |
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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. |
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dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
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dc.rights.uri |
https://www.elsevier.com/journals/advances-in-mathematics/0001-8708/guide-for-authors#13300 |
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dc.subject |
Science & Technology |
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dc.subject |
Physical Sciences |
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dc.subject |
Mathematics |
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dc.subject |
Finite group |
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dc.subject |
Sylow subgroup |
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dc.subject |
Element orders |
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dc.subject |
FINITE GROUPS |
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dc.subject |
P-SUBGROUP |
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dc.subject |
CRITERION |
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dc.subject |
ELEMENT |
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dc.subject |
BELONG |
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dc.title |
Answer to a 1962 question by Zappa on cosets of Sylow subgroups |
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dc.type |
Journal Article |
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dc.identifier.doi |
10.1016/j.aim.2017.04.011 |
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pubs.begin-page |
167 |
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pubs.volume |
313 |
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dc.rights.holder |
Copyright: Elsevier |
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pubs.author-url |
http://www.sciencedirect.com/science/article/pii/S0001870816315778 |
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pubs.end-page |
175 |
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pubs.publication-status |
Published |
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dc.rights.accessrights |
http://purl.org/eprint/accessRights/OpenAccess |
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pubs.subtype |
Article |
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pubs.elements-id |
624458 |
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pubs.org-id |
Science |
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pubs.org-id |
Mathematics |
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dc.identifier.eissn |
1090-2082 |
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pubs.record-created-at-source-date |
2019-07-08 |
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pubs.online-publication-date |
2017-05-16 |
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