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Minimal Relations for Certain Wreath Products of Groups

Published online by Cambridge University Press:  20 November 2018

D. L. Johnson
D. L. Johnson*
Affiliation:
University of Nottingham, Nottingham, England
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Let p be a rational prime, G a non-trivial finite p group, and K the field of p elements, regarded as a trivial G-module according to context; then we define:

d(G) = dimKH1(G, K), the minimal number of generators of G,

r(G) = dimKH2(G, K),

r′(G) = the minimal number of relations required to define G,

where, in the last equation, it is sufficient to take the minimum over those presentations of G with d(G) generators. It is well known (see § 2) that the following inequalities hold:

We shall consider only finite p-groups, so that the class of groups with r = d coincides with that consisting of those groups whose Schur multiplicator is trivial.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 1005 - 1009
Copyright
Copyright © Canadian Mathematical Society 1970

References

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