Bounding the order of a group with a large conjugacy class

In this paper, we present results for a group theoretic analog to a parameter defined in terms of irreducible character degrees. Let be a finite group and be the size of the largest conjugacy class of . The parameter is defined by the equation . We show that where is the smallest prime dividing the...

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Bibliographic Details
Published inJournal of group theory Vol. 18; no. 2; pp. 201 - 207
Main Author Harrison, Anthony W.
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.03.2015
Walter de Gruyter GmbH
Subjects
Classification
Group theory
Mathematical analysis
Parameters
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Summary:In this paper, we present results for a group theoretic analog to a parameter defined in terms of irreducible character degrees. Let be a finite group and be the size of the largest conjugacy class of . The parameter is defined by the equation . We show that where is the smallest prime dividing the order of and classify groups that satisfy this bound.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1433-5883
1435-4446
DOI:10.1515/jgth-2014-0033