Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-16T04:54:12.452Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Extract

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.

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

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

REFERENCES

[1]Bourbaki, N.. Éléments de Mathématique, XXXIV: Groupes et Algébres de Lie, Chap. IV (Hermann, 1968).Google Scholar
[2]Chiswell, I. M., Collins, D. J. and Huebschmann, J.. Aspherical group presentations. Math. Z. 178 (1981), 1–36.CrossRefGoogle Scholar
[3]Collins, D. J. and Huebschmann, J.. Spherical diagrams and identities among relations. Math. Ann. 261 (1982), 155–183.CrossRefGoogle Scholar
[4]Gruenberg, K. W.. Cohomological Topics in Group Theory. Lecture Notes in Math. vol. 143 (Springer-Verlag, 1970).CrossRefGoogle Scholar
[5]Howie, J.. Cohomology of one relator products of locally indicable groups, to appear in J. London Math. Soc.Google Scholar
[6]Huebschmann, J.. Cohomology theory of aspherical groups and of small cancellation groups. J. Pure Appl. Algebra 14 (1979), 137–143.CrossRefGoogle Scholar
[7]Lyndon, R. C.. On Dehn's algorithm. Math. Ann. 166 (1966), 208–228.CrossRefGoogle Scholar
[8]Lyndon, R. C. and Schupp, P. E.. Combinatorial Group Theory. Ergebnisse der Math., Bd 89 (Springer-Verlag, 1977).Google Scholar
[9]McCool, J.. Elements of finite order in free product sixth-groups. Glasgow Math. J. 9 (1969), 128–145.CrossRefGoogle Scholar
[10]Schupp, P. E.. On Greendlinger's Lemma. Comm. Pure. Appl. Math. 23 (1970), 233–240.CrossRefGoogle Scholar
[11]Schupp, P. E.. A survey of small cancellation theory. In Word Problems, pp. 569–589 (North-Holland, 1973).Google Scholar