We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Bloch-Kato pro- p groups and locally powerful groups.
- Authors
Quadrelli, Claudio
- Abstract
A Bloch-Kato pro- p group G is a pro- p group with the property that the -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 such that G is θ-abelian. In case that G is also finitely generated, this implies that G is powerful, p-adic analytic with , and its -cohomology ring is an exterior algebra. These results will be obtained by studying locally powerful groups. 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. Finally, we study certain closure operations of the class of Bloch-Kato pro- p groups, connected with the Elementary Type Conjecture.
- Subjects
GROUP theory; GALOIS cohomology; ALTERNATIVE algebras; AUSDEHNUNGSLEHRE; COHOMOLOGY theory
- Publication
Forum Mathematicum, 2014, Vol 26, Issue 3, p793
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2011-0069