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The Reidemeister-Schreier and Kuroš subgroup theorems

Published online by Cambridge University Press:  26 February 2010

A. J. Weir
A. J. Weir
Affiliation:
Queen Mary College, University of London.
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Extract

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.

Type
Research Article
Information
Mathematika , Volume 3 , Issue 1 , June 1956 , pp. 47 - 55
Copyright
Copyright © University College London 1956

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References

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