Arithmetic results on orbits of linear groups

Persistent Link:
http://hdl.handle.net/10150/614975
Title:
Arithmetic results on orbits of linear groups
Author:
Giudici, Michael; Liebeck, Martin W.; Praeger, Cheryl E.; Saxl, Jan; Tiep, Pham Huu
Affiliation:
Univ Arizona, Dept Math
Issue Date:
2015-08-19
Publisher:
AMER MATHEMATICAL SOC
Citation:
Arithmetic results on orbits of linear groups 2015, 368 (4):2415 Transactions of the American Mathematical Society
Journal:
Transactions of the American Mathematical Society
Rights:
First published in Trans. Amer. Math. Soc. 368 (April 2016), published by the American Mathematical Society. Copyright 2015 American Mathematical Society.
Collection Information:
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
Abstract:
Let p be a prime and G a subgroup of GL(d)(p). We define G to be p-exceptional if it has order divisible by p, but all its orbits on vectors have size coprime to p. We obtain a classification of p-exceptional linear groups. This has consequences for a well-known conjecture in representation theory, and also for a longstanding question concerning 1/2-transitive linear groups (i.e. those having all orbits on nonzero vectors of equal length), classifying those of order divisible by p.
Note:
Article electronically published on August 19, 2015.
ISSN:
0002-9947; 1088-6850
DOI:
10.1090/tran/6373
Version:
Final accepted manuscript
Sponsors:
The first four authors acknowledge the support of an ARC Discovery Grant; the first author acknowledges the support of an Australian Research Fellowship; the third author acknowledges the support of a Federation Fellowship; the fifth author acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374).
Additional Links:
http://www.ams.org/tran/2016-368-04/S0002-9947-2015-06373-9/

Full metadata record

DC FieldValue Language
dc.contributor.authorGiudici, Michaelen
dc.contributor.authorLiebeck, Martin W.en
dc.contributor.authorPraeger, Cheryl E.en
dc.contributor.authorSaxl, Janen
dc.contributor.authorTiep, Pham Huuen
dc.date.accessioned2016-06-28T23:42:34Z-
dc.date.available2016-06-28T23:42:34Z-
dc.date.issued2015-08-19-
dc.identifier.citationArithmetic results on orbits of linear groups 2015, 368 (4):2415 Transactions of the American Mathematical Societyen
dc.identifier.issn0002-9947-
dc.identifier.issn1088-6850-
dc.identifier.doi10.1090/tran/6373-
dc.identifier.urihttp://hdl.handle.net/10150/614975-
dc.description.abstractLet p be a prime and G a subgroup of GL(d)(p). We define G to be p-exceptional if it has order divisible by p, but all its orbits on vectors have size coprime to p. We obtain a classification of p-exceptional linear groups. This has consequences for a well-known conjecture in representation theory, and also for a longstanding question concerning 1/2-transitive linear groups (i.e. those having all orbits on nonzero vectors of equal length), classifying those of order divisible by p.en
dc.description.sponsorshipThe first four authors acknowledge the support of an ARC Discovery Grant; the first author acknowledges the support of an Australian Research Fellowship; the third author acknowledges the support of a Federation Fellowship; the fifth author acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374).en
dc.language.isoenen
dc.publisherAMER MATHEMATICAL SOCen
dc.relation.urlhttp://www.ams.org/tran/2016-368-04/S0002-9947-2015-06373-9/en
dc.rightsFirst published in Trans. Amer. Math. Soc. 368 (April 2016), published by the American Mathematical Society. Copyright 2015 American Mathematical Society.en
dc.titleArithmetic results on orbits of linear groupsen
dc.typeArticleen
dc.contributor.departmentUniv Arizona, Dept Mathen
dc.identifier.journalTransactions of the American Mathematical Societyen
dc.description.noteArticle electronically published on August 19, 2015.en
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en
dc.eprint.versionFinal accepted manuscripten
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