Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-17T14:49:41.636Z Has data issue: false hasContentIssue false
  • English
  • Français

A proof of the subgroup theorem for free products

Published online by Cambridge University Press:  26 February 2010

Saunders Maclane†
Saunders Maclane†
Affiliation:
University of Chicago, Chicago 37, Ill., U.S.A.
Get access

Extract

For each index β in a set J let Aβ be a group. The free product

is by definition a group generated by the Aβ in which any two distinct reduced words represent distinct elements. Here a reduced word is either the expression 1 or an expression

with each “syllable” ai ≠ 1 and each βi ≠ βi+1.

Type
Research Article
Information
Mathematika , Volume 5 , Issue 1 , June 1958 , pp. 13 - 19
Copyright
Copyright © University College London 1958

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.)

References

1.Baer, R. and Levi, R., “Freie Produkte und ihre Untergruppen”, Comp. Math., 3 (1938), 391–398.Google Scholar
2.Hall, Marshall Jr., “Subgroups of free products”, Pacific Journal of Mathematics, 3 (1953), 115–120.CrossRefGoogle Scholar
3.Hurewicz, Witold, “Zu einer Arbeit von O. Schreier”, Hamburg Abh., 8 (1930), 307–314.CrossRefGoogle Scholar
4.Kuhn, Harold W., “Subgroup theorems for groups presented by generators and relations”, Ann. of Math., 56 (1952), 22–41.CrossRefGoogle Scholar
5.Kurosh, A. G., “Die Untergruppen der freien Produkte von beliebigen Gruppen”, Math. Ann., 109 (1934), 647–660.CrossRefGoogle Scholar
6.Kurosh, A. G., The Theory of Groups, translated by Hirsch, K. A. (New York, 1955).Google Scholar
7.Specht, Wilhelm, Gruppentheorie (Berlin-Göttingen-Heidelberg, 1956).Google Scholar
8.Takahasi, M., “Bemerkungen über den Untergruppensatz in freien Produkte”, Proc. Acad. Tokyo, 20 (1945), 589–594.Google Scholar
9.Weir, A. J., “The Reidemeister-Schreier and Kurosh subgroup theorems”, Mathematika, 3 (1956), 47–55.CrossRefGoogle Scholar