Strongly free sequences and pro-p-groups of cohomological dimension 2

Higher Massey products in the cohomology of mild pro-p-groups

“…This is shown in [1], Th.3.2 in the case of lexicographic orders < defined as in 3.4. As has been remarked by P. Forré in [7], Th.2.6, the proof immediately carries over to arbitrary multiplicative orders.…”

“…has rank m. (III) If p = 3, then a n i = 0 if c < i and 1 ≤ n ≤ m. These conditions resemble [20], Th.5.5 and [7], Cor.6.5 respectively, where similar statements for relations of degree 2 are given.…”

Koszul algebras and quadratic duals in Galois cohomology

“…The concept of mild group has been introduced by J. Labute in [Lab85] and D. Anick in [Ani87] as groups whose relators are as independent as possible with respect to the lower central series. Mild pro-p groups were subsequently defined for several filtrations in [Lab06], for p odd, and in [LM11] and [For11], for p = 2. It came as a surprise when J. Labute discovered that these groups have cohomological dimension 2 and some occur naturally as Galois groups of maximal p-extensions with restricted ramification.…”

On the Invariant Factors of Class Groups in Towers of Number Fields

“…We note that Labute (Theorem 1.6 of [19]) was the first to give a sufficient condition for mildness of G T S ; thanks to the work of Schmidt [30], for any K, by choosing S large enough, one can arrange that the group G T S is of cohomological dimension 2 and mild, hence meets the conditions of the Theorem. (See also the work of Labute [19], Forré [6], Gärtner [8], Vogel [33], etc.) We wish to highlight the fact that the preceding Theorem combines together some results from analytic number theory (Brauer-Siegel), arithmetic (the results of Schmidt and the fact that the root discriminant is bounded) and group theory!…”