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Conjugacy classes in finite groups

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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.

Summary

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.

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  1. School of Mathematical Sciences Raymond and Beverly Sacler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv, Israel

    Marcel Herzog

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  1. Marcel Herzog
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(Conferenza tenuta il 13 febbraio 1990)

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Herzog, M. Conjugacy classes in finite groups. Seminario Mat. e. Fis. di Milano 60, 9–14 (1990). https://doi.org/10.1007/BF02925075

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