Conjugacy classes in finite groups

  • Marcel Herzog


LetG be a finite group withk conjugacy classes. Thenk>log 2log2|G| and ifG is a simple non-abelian group then\(k< \tfrac{{|G|lnln|G|}}{{ln|G|}}\).

If Γ (G) is the graph with the non-central conjugacy classes as vertices and two classesC 1 andC 2 are joined by an edge if (|C 1|, |C 2|)>1 then Γ (G) has at most 2 connected components.


Finite Group Conjugacy Class Nilpotent Group Solvable Group Frobenius Group 
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SiaG un gruppo finito conk classi di conuigio. Allorak>log 2log2|G| e seG è un gruppo semplice non-abeliano allora\(k< \tfrac{{|G|lnln|G|}}{{ln|G|}}\).

Se Γ (G) è il grafo avente come vertici le classi di coniugio non centrali e in cui due classiC 1 eC 2 sono unite da un lato se (|C 1|, |C 2|)>1, allora Γ (G) ha al più 2 componenti connesse.


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Copyright information

© Birkhäuser-Verlag 1990

Authors and Affiliations

  • Marcel Herzog
    • 1
  1. 1.School of Mathematical Sciences Raymond and Beverly Sacler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael

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