Hostname: page-component-cb9f654ff-qc88w Total loading time: 0 Render date: 2025-08-21T10:50:39.042Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Sohreier, O., Abh. Math. Sem. Hamburg Univ., 5 (1927), 161–183.CrossRefGoogle Scholar
2.Kurosoh, A., Math. Ann., 109 (1934), 647–660.CrossRefGoogle Scholar
3.Baer, R. and Levi, F., Compositio Math., 3 (1936), 391–398.Google Scholar
4.Takahasi, M., Proc. Imp. Acad. Tokyo, 20 (1944), 589–594.Google Scholar
5.Hall, M., Pacific Journal of Math., 3 (1953), 115–120.CrossRefGoogle Scholar
6.Kuhn, H. W., Annals of Math., 56 (1952), 22–46.CrossRefGoogle Scholar
7.Fox, R. H., Annals of Math., 57 (1953), 547–560; 59 (1954), 196–210.CrossRefGoogle Scholar
8.Kuroš, A., Theory of Groups (Chelsea, New York, 1956), vol. 2, §33.Google Scholar