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Conjugacy classes in finite groups

Published online by Cambridge University Press:  14 November 2011

Antonio Vera López
Antonio Vera López
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad del Pais Vasco, Apartado 644, Bilbao, Spain
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Synopsis

In this paper, the number of conjugacy classes in a finite group G is analysed in terms of the number of ordered pairs that generate it. Using this relation, we give a new elementary proof of one of A. Mann's results for finite groups, namely: |G| ≡ r(G) (mod. d|G|. δ|G|), where , prime and pi ≠ Pj for every i≠j, r(G) denotes the number of conjugacy classes of elements of G, d|G| = g.c.d. (p1 − 1, … pt − 1) and δ|G| = g.c.d. . The above congruence is obtained without using character theory. We also obtain new local congruences that slightly improve Mann's congruence.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 259 - 264
Copyright
Copyright © Royal Society of Edinburgh 1987

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