Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bloch-Kato pro-p groups and locally powerful groups   A Bloch-Kato pro-p group G is a pro-p group with the property that the
F_p-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 $\theta\colon G\rightarrow
\Z_p^\times$ such that G is theta-abelian. In case that G is also finitely
generated, this implies that G is powerful, p-adic analytic with d(G)=cd(G),
and its \F_p-cohomology ring is an exterior algebra. These results will be
obtained by studying locally powerful groups (see Theorem 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.

25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat