1,721,136 research outputs found
Weigel, T[heodor] O[swald] an Herman Grimm (1 Brief)
No full textWEIGEL, T[HEODOR] O[SWALD] AN HERMAN GRIMM (1 BRIEF)
Weigel, T[heodor] O[swald] an Herman Grimm (1 Brief) (Br5453)
Brief 5453 (Br5453
Profinite Groups with a Cyclotomic p-Orientation
Full text linkProfinite groups with a cyclotomic p-orientation are introduced and studied. The special interest in this class of groups arises from the fact that any absolute Galois group GK of a field K is indeed a profinite group with a cyclotomic p-orientation θK,p:GK→Z×p which is even Bloch-Kato. The same is true for its maximal pro-p quotient GK(p) provided the field K contains a primitive pth-root of unity. The class of cyclotomically p-oriented profinite groups (resp. pro-p groups) which are Bloch-Kato is closed with respect to inverse limits, free product and certain fibre products. For profinite groups with a cyclotomic p-orientation the classical Artin-Schreier theorem holds. Moreover, Bloch-Kato pro-p groups with a cyclotomic orientation satisfy a strong form of Tits' alternative, and the elementary type conjecture formulated by I. Efrat can be restated that the only finitely generated indecomposable torsion free Bloch-Kato pro-p groups with a cyclotomic orientation should be Poincaré duality pro-p groups of dimension less or equal to 2
Oriented pro-l groups with the Bogomolov-Positselski property
Full text linkFor a prime number l we say that an oriented pro-l group (G,θ) has the Bogomolov-Positselski property if the kernel of the canonical projection on its maximal θ-abelian quotient π:G→G(θ) is a free pro-l group contained in the Frattini subgroup of G. We show that oriented pro-l groups of elementary type have the Bogomolov-Positselski property. This shows that Efrat's Elementary Type Conjecture implies a positive answer to Positselski's version of Bogomolov's Conjecture on maximal pro-l Galois groups of a field K in case that K*/(K*)l is finite. Secondly, it is shown that for an H*-quadratic oriented pro-l group (G,θ) the Bogomolov-Positselski property can be expressed by the injectivity of the transgression map in the Hochschild-Serre spectral sequence
- …
