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An inequality for group presentations

Published online by Cambridge University Press:  17 April 2009

Avionam Mann
Avionam Mann
Affiliation:
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel e-mail: [email protected]
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Abstract

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To Bernhard Neumann on his 90th Birthday

We prove an inequality involving the number of relations and of relations and of generators of any group, and derive some consequences. The proof applies the theory of pro-p groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 467 - 469
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Baumslag, G., Topics in combinatorial group theory (Birkhaüser, Basel, 1993).CrossRefGoogle Scholar
[2]Dixon, J.D., du Sautoy, M.P.F., Mann, A. and Segal, D., Analytic Pro-p groups, 2nd ed. (Cambridge University Press, Cambrdige, 1999).CrossRefGoogle Scholar
[3]Gaschütz, W. and Newman, M.F., ‘On presentations of finite p-groups’, J. Reine Angew. Math. 245 (1970), 172–176.Google Scholar
[4]Neumann, B.H., On some finite groups with trivial multiplicator, Publ. Math. 4 (1956), 190–194.Google Scholar