The structure of finite groups with three class sizes

Beltrán, Antonio; Felipe, María José

doi:10.1515/jgt.2008.095

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…We note that the results in [BF09] can be deduced from the results of Dolfi & Jabara. This completes the classification of groups of conjugate rank 2.…”

Section: Ar Camina's Theorem Says What Happens If This Does Not Occurmentioning

confidence: 51%

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The Influence of Conjugacy Class Sizes on the Structure of Finite Groups: A Survey

Camina

Camina²

2011

Asian-European J. Math.

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The importance of conjugacy classes for the structure of finite groups was recognised very early in the study of groups. In this survey we consider the results from the many articles which have developed this topic and examined the influence of conjugacy class sizes or the number of conjugacy classes on the structure of finite groups. Whilst we begin by mentioning the early results of Sylow and Burnside, our major objective is to highlight the more recent work and present some interesting questions which we hope will inspire further research

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“…We note that the results in [BF09] can be deduced from the results of Dolfi & Jabara. This completes the classification of groups of conjugate rank 2.…”

Section: Ar Camina's Theorem Says What Happens If This Does Not Occurmentioning

confidence: 51%

“…Their proof is independent of [31] but uses [86]: We note that the results in [21] can be deduced from the results of Dolfi & Jabara. This completes the classification, up to nilpotent groups, which in this context means p-groups, of groups of conjugate rank 2.…”

Section: Theorem 35 [31]mentioning

confidence: 81%

The Influence of Conjugacy Class Sizes on the Structure of Finite Groups: A Survey

Camina

Camina²

2011

Asian-European J. Math.

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“…By [4,Corollary 6], P/Z(P ) has exponent p . Since Z(P ) ≤ P 0 , we have that P/P 0 also has exponent p .…”

Section: Is a Frobenius Group With |H/z(g)mentioning

confidence: 99%

Finite groups with three conjugacy class sizes of primary and biprimary elements

Shao¹,

Jiang²

2015

Turk J Math

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Structure of $$p$$ -complements in groups with three $$p$$ -regular class sizes

Beltrán

Felipe

2012

Monatsh Math

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The structure of finite groups with three class sizes

Cited by 6 publications

References 13 publications

The Influence of Conjugacy Class Sizes on the Structure of Finite Groups: A Survey

The Influence of Conjugacy Class Sizes on the Structure of Finite Groups: A Survey

Finite groups with three conjugacy class sizes of primary and biprimary elements

Structure of $$p$$ -complements in groups with three $$p$$ -regular class sizes

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