Hostname: page-component-5b777bbd6c-sbgtn Total loading time: 0 Render date: 2025-06-23T06:32:26.434Z Has data issue: false hasContentIssue false
  • English
  • Français

Relation modules of amalgamated free products and HNN extensions

Published online by Cambridge University Press:  18 May 2009

Torsten Hannebauer
Torsten Hannebauer
Affiliation:
Humboldt-Universität zu Berlin, Sektion Mathematik, Unter den Linden 6, Berlin, GDR—1086
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a group and

a free presentation of G, i.e. a short exact sequence of groups with F free. Conjugation in F induces on = R/R', the abelianized normal subgroup R, the structure of a right G-module (if r∈ R, x∈ F then (r)(xπ) = x-1rxR'). The G-module is called the relation module determined by the presentation (1). For a detailed discussion of this subject we refer to Gruenberg [3].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 3 , September 1989 , pp. 263 - 270
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Bieri, R., Mayer-Vietoris sequences for HNN groups and homological duality, Math. Z. 143 (1975), 123–130.CrossRefGoogle Scholar
2.Gruenberg, K. W., Cohomological topics in group theory, Lecture Notes in Mathematics 143 (Springer, 1970).CrossRefGoogle Scholar
3.Gruenberg, K. W., Relation modules of finite groups, CBMS Regional Conference Series in Mathematics 25 (Providence, 1976).CrossRefGoogle Scholar
4.Hilton, J. P. and Stammbach, U., A course in homological algebra, Graduate Texts in Mathematics 4 (Springer, 1971).CrossRefGoogle Scholar
5.Lyndon, R. C. and Schupp, P. E., Combinatorial group theory (Springer, 1977).Google Scholar
6.Stammbach, U., Homology in group theory, Lecture Notes in Mathematics 359 (Springer, 1973).CrossRefGoogle Scholar