On a new characterization of Demuskin groups

Pro-p groups of rank 3 and the question of Iwasawa

“…According to Dummit and Labute (see [3]), Iwasawa observed that pro-p groups that belong to the class E n for a fixed positive integer n have interesting representation-theoretic properties and he raised the question of determining those groups with n = 1. In [3] Dummit and Labute answered this question for 1-relator groups in the case n = 2. Actually they proved that G is a Demushkin group if and only if G is a one relator group and G ∈ E 2 .…”

Positively ramified extensions of algebraic number fields.

“…is totally decomposed in the extension L'/L^a simple calcu- The result now follows from the main theorem of [2]. We show that, if C p eL and the group Gal(L(p)/L ao ) is nontrivial, then it is a Demushkin group.…”

Demuškin groups, Galois modules, and the Elementary Type Conjecture

“…In the proof of Theorem 1 we cited [DuLa,Theorem 1] (N, F p ) in the case of strongly regular not totally degenerate p-quaternionic pairings. There is some additional interest in this formulation because p-quaternionic pairings which are strongly regular but not weakly p-local have been abstractly constructed (see [Ku2,Theorem 9]), and it is not known whether these pairings are realizable as γ F for suitable fields F .…”