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Cohomology and finite subgroups of small cancellation quotients of free products

Published online by Cambridge University Press:  24 October 2008

Donald J. Collins  and
Jean Perraud
Donald J. Collins
Affiliation:
School of Mathematical Sciences, Queen Mary College, London E1 4NS and Institut de Mathématique et d'informatique, Université de Nantes, 44072 Nantes–Cedex, France
Jean Perraud
Affiliation:
School of Mathematical Sciences, Queen Mary College, London E1 4NS and Institut de Mathématique et d'informatique, Université de Nantes, 44072 Nantes–Cedex, France
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In this paper we study small cancellation quotients of free products. In particular we calculate their cohomology and, via a theorem of Serre, classify their finite subgroups. The results obtained are the natural analogues of the corresponding results for small cancellation quotients of free groups obtained in Huebschmann [6] (but see also Collins-Huebschmann[3]). They also generalize results of McCool[9] on elements of finite order in quotients of free products and similar conclusions have been obtained by Howie [5] for one-relator quotients of free products of locally indicable groups.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 243 - 259
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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