A recursive description of pro-p Galois groups

Engler, Antonio José

doi:10.1016/j.jalgebra.2003.12.014

Cited by 2 publications

(2 citation statements)

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“…Some time ago I. Efrat has formulated a conjecture -the so called "elementary type conjecture" -for maximal pro-p Galois groups, which states that the group structure of maximal pro-p Galois groups of some fields is very restricted, namely such groups are free pro-p products and semidirect products of certain pro-p groups (see [9], [12]).…”

Section: The Class Of Bloch-kato Pro-p Groupsmentioning

confidence: 99%

Bloch–Kato pro-p groups and locally powerful groups

Quadrelli¹

2012

Forum Mathematicum

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A Bloch-Kato pro-p group G is a pro-p group with the property that the Fp-cohomology ring of every closed subgroup of G is quadratic. It is shown that either such a pro-p group G contains no closed free pro-p groups of infinite rank, or there exists an orientation θ : G → Z × p such that G is θabelian. (See Thm B.) In case that G is also finitely generated, this implies that G is powerful, p-adic analytic with d(G) = cd(G), and its Fp-cohomology ring is an exterior algebra (see Cor. 4.8). These results will be obtained by studying locally powerful groups (see Thm A). There are certain Galois-theoretical implications, since Bloch-Kato pro-p groups arise naturally as maximal pro-p quotients and pro-p Sylow subgroups of absolute Galois groups (see Corollary 4.9). Finally, we study certain closure operations of the class of Bloch-Kato pro-p groups, connected with the Elementary type conjecture.

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Section: The Class Of Bloch-kato Pro-p Groupsmentioning

confidence: 99%

Bloch–Kato pro-p groups and locally powerful groups

Quadrelli¹

2012

Forum Mathematicum

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“…The Elementary Type Conjecture for p > 2 is then as follows. (We note that there are several variants of the Elementary Type Conjecture which aim at the classification of finitely generated Gal(F (p)/F ), contained in [Ef1,Ef2,En,JW], and [Ma1,p. 123].…”

Section: P-quaternionic Pairings and The Elementary Type Conjecturementioning

confidence: 99%