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Conjugacy expansiveness in finite groups
-
Zoltán Halasi
,
Attila Maróti
Published/Copyright:
June 29, 2012
Abstract.
A finite group G is called expansive if for every normal set S
and every conjugacy class C of G the normal set 
consists
of at least as many conjugacy classes of G as S does. This
notion is motivated by a finiteness criterion. It is shown that a
group is expansive if and only if it is a direct product of
expansive simple or abelian groups. The groups 
and 
are expansive for every 
and every
respectively. Many small simple groups
including all sporadic simple groups are also expansive.
Received: 2011-10-28
Revised: 2012-02-02
Published Online: 2012-06-29
Published in Print: 2012-07-01
© 2012 by Walter de Gruyter Berlin Boston
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- Masthead
- Degrees, class sizes and divisors of character values
- On p-group Camina pairs
- Conjugacy expansiveness in finite groups
- Zero excess and minimal length in finite Coxeter groups
- Second order Dehn functions of Pride groups
- Some skew linear groups with Engel's condition
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Articles in the same Issue
- Masthead
- Degrees, class sizes and divisors of character values
- On p-group Camina pairs
- Conjugacy expansiveness in finite groups
- Zero excess and minimal length in finite Coxeter groups
- Second order Dehn functions of Pride groups
- Some skew linear groups with Engel's condition
- Irreducible representations of Baumslag–Solitar groups
- On generators of crystallographic groups and actions on flat orbifolds
- Corrigendum Spinal groups: semidirect product decompositions and Hausdorff dimension [J. Group Theory 14 (2011), 491–519]
