Geodesic
Classification of Demushkin Groups
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 106-132

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

A pro-p-group G is said to be a Demushkin group if (1) dimFp H1(G, Z/pZ) < ∞, (2) dimFp H2(G, Z/pZ) = 1, (3) the cup product H1(G, Z/pZ) × H1(G, Z/pZ) → H2(G, Z/pZ) is a non-degenerate bilinear form. Here FP denotes the field with p elements. If G is a Demushkin group, then G is a finitely generated topological group with n(G) = dim H1(G, Z/pZ) as the minimal number of topological generators; cf. §1.3. Condition (2) means that there is only one relation among a minimal system of generators for G; that is, G is isomorphic to a quotient F/(r), where F is a free pro-p-group of rank n = n(G) and (r) is the closed normal subgroup of F generated by an element r ∈ F9 (F, F); cf. §1.4. 
Labute, John P. Classification of Demushkin Groups. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 106-132. doi: 10.4153/CJM-1967-007-8
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