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On class numbers of a finite group and of its subgroups*

Published online by Cambridge University Press:  14 November 2011

A. Vera-López  and
J. Sangroniz
A. Vera-López
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad del Pais Vasco, Apartado 644, Bilbao, Spain
J. Sangroniz
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad del Pais Vasco, Apartado 644, Bilbao, Spain
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Synopsis

In this paper we obtain new results which relate the number of conjugacy classes of л-elements of a finite group and an arbitrary subgroup, which are analogous to some results about normal subgroups. We also prove some new results which show the relationship between class numbers and splitting theorems. Our proofs only involve elementary techniques.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 2 , 1993 , pp. 295 - 301
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Chillag, D. and Herzog, M.. On the length of the conjugacy classes of finite groups. J. Algebra 131 (1990), 110–125.CrossRefGoogle Scholar
2Ernest, J. A.. Central intertwining numbers for representations of finite groups. Trans. Amer. Math. Soc. 99 (1961), 499–508.CrossRefGoogle Scholar
3Gallagher, P. X.. The number of conjugacy classes in a finite group. Math. Z. 118 (1970) 175–179.Google Scholar
4Nagao, H. and Tsushima, Y.. Representations of finite groups (San Diego: Academic Press, 1989).Google Scholar
5Rose, J. S.. A Course on Group Theory (Cambridge: Cambridge Univ. Press, 1978).Google Scholar
6Vera-Lopez, A. and Ortiz de Elguea, L.. On the number of conjugacy classes in a finite group. J. Algebra 115 (1988), 46–74.CrossRefGoogle Scholar