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Common Transversals

Published online by Cambridge University Press:  20 January 2009

R. A. Rankin
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A well-known theorem in group theory [(8), p. 11, Satz 3] asserts that, when H is a subgroup of finite index in a group G, there exists a system of common representatives of the right cosets and the left cosets of H in G. Various proofs and generalisations, mainly involving combinatorial rather than grouptheoretical ideas, are known, and an excellent account of the subject is to be found in Chapter 5 of Ryser's book (6), where references to the literature are given. The purpose of the present paper is to use group-theoretical ideas to prove theorems of a similar nature. The motivation for this work comes from the theory of Hecke operators, and one of the main objects is to provide a simple proof of a result given by Petersson (4), which is needed in order to prove the normality of these operators.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 2 , December 1966 , pp. 147 - 154
Copyright
Copyright © Edinburgh Mathematical Society 1966

References

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