Geodesic
Minimal Relations for Certain Wreath Products of Groups
Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 1005-1009

Voir la notice de l'article provenant de la source Cambridge University Press

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) = dimK H 1(G, K), the minimal number of generators of G, r(G) = dimK H 2(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. 
Johnson, D. L. Minimal Relations for Certain Wreath Products of Groups. Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 1005-1009. doi: 10.4153/CJM-1970-116-2
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