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The Reidemeister-Schreier and Kuroš subgroup theorems

  • A. J. Weir (a1)

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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