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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Dey, I. M. S. 1965. Schreier systems in free products. Proceedings of the Glasgow Mathematical Association, Vol. 7, Issue. 02, p. 61.

    Higgins, P. J. 1964. Presentations of groupoids, with applications to groups. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 60, Issue. 01, p. 07.

    Cohen, D. E. 1960. Certain subgroups of free products. Mathematika, Vol. 7, Issue. 02, p. 117.

    Karrass, A. and Solitar, D. 1958. Subgroup theorems in the theory of groups given by defining relations. Communications on Pure and Applied Mathematics, Vol. 11, Issue. 4, p. 547.

    Maclane†, Saunders 1958. A proof of the subgroup theorem for free products. Mathematika, Vol. 5, Issue. 01, p. 13.


The Reidemeister-Schreier and Kuroš subgroup theorems

  • A. J. Weir (a1)
  • DOI:
  • Published online: 01 February 2010

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.

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1.O. Sohreier , Abh. Math. Sem. Hamburg Univ., 5 (1927), 161183.

2.A. Kurosoh , Math. Ann., 109 (1934), 647660.

4.M. Takahasi , Proc. Imp. Acad. Tokyo, 20 (1944), 589594.

5.M. Hall , Pacific Journal of Math., 3 (1953), 115120.

6.H. W. Kuhn , Annals of Math., 56 (1952), 2246.

7.R. H. Fox , Annals of Math., 57 (1953), 547560; 59 (1954), 196–210.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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