Common Transversals
R. A. Rankin · Proceedings of the Edinburgh Mathematical Society · 1966
A well-known theorem in group theory [(8), p. 11, Satz 3] asserts that, whenHis a subgroup of finite index in a groupG, there exists a system of common representatives of the right cosets and the left cosets ofHinG. 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.