Mathematika

Research Article

The Reidemeister-Schreier and Kuroš subgroup theorems

A. J. Weira1

a1 Queen Mary College, University of London.

If a group G is presented in terms of generators and relations, then the classical Reidemeister-Schreier Theorem [1] gives a presentation for any subgroup of G. If G is a free product of groups Gα each of which is presented in terms of generators and relations, then the main result of this paper is a presentation for any subgroup H of G, which shows the nature of H as a free product of certain subgroups of G. This result is a generalization of the celebrated Kuroš Theorem [2]. It also includes the Reidemeister–Schreier Theorem and the Schreier Theorem [1] which states that any subgroup of a free group is free.

(Received November 10 1955)