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Explicit generators for the relation module in the example of Gruenberg–Linnell

Published online by Cambridge University Press:  07 March 2016

W. H. MANNAN
W. H. MANNAN*
Affiliation:
School of Computing, Engineering and Mathematics, University of Brighton, Cockroft Building, Lewes Road, Brighton BN2 4GJ. e-mail: wajid@mannan.info
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Abstract

Gruenberg and Linnell showed that the standard relation module of a free product of n groups of the form Cr × $\mathbb{Z}$ could be generated by just n + 1 generators, raising the possibility of a relation gap. We explicitly give such a set of generators.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 2 , September 2016 , pp. 199 - 202
Copyright
Copyright © Cambridge Philosophical Society 2016 

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References

REFERENCES

[1] Bridson, M. R. and Tweedale, M. Deficiency and abelianised deficiency of some virtually free groups. Math. Proc. Camb. Phil. Soc. 143 (2007), 257–264.CrossRefGoogle Scholar
[2] Edwards, T. Generalised Swan modules and the D2 problem. Algebr. Geom. Topol. 6 (2006), 71–89.Google Scholar
[3] Gruenberg, K. and Linnell, P. Generation gaps and abelianized defects of free products. J. Group Theory 11 (5) (2008), 587–608.CrossRefGoogle Scholar
[4] Harlander, J. Some aspects of efficiency. In Groups–Korea'98, Pusan (de Gruyter, 2000), pp. 165–180.Google Scholar
[5] Hog-Angeloni, C. Beiträge zum (einfachen) Homotopietyp bei freien Produkten und anderen gruppentheoretischen Konstruktionen. PhD. thesis. Johann Wolfgang Goethe–Universität Frankfurt am Main (1988).Google Scholar
[6] Johnson, F.E.A. Stable Modules and the D(2) Problem. Lecture Note Series 301 (LMS, 2003).CrossRefGoogle Scholar
[7] Mannan, W.H. Realizing algebraic 2-complexes by cell complexes. Math. Proc. Camb. Phil. Soc. 14 (2009), 671–673.CrossRefGoogle Scholar
[8] Mannan, W.H. Quillen's plus construction and the D(2) problem. Algebr. Geom. Topol. 9 (2009), 1399–1411.CrossRefGoogle Scholar