Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Successive approximation of p-class towers   Let F be a number field and p be a prime. In the Successive Approximation
Theorem, we prove that, for each positive integer n, finitely many candidates
for the Galois group G(p,n,F) of the n-th stage F(p,n) of the p-class tower
F(p,infinity) over F are determined by abelian type invariants of p-class
groups Cl(p,E) of unramified extensions E/F with degree [E:F]=$p^{n-1}$.
Illustrated by the most extensive numerical results available currently, the
transfer kernels ker(T(F,E)) of the p-class extensions T(F,E):Cl(p,F)-->Cl(p,E)
from F to unramified cyclic degree-p extensions E/F are shown to be capable of
narrowing down the number of contestants significantly. By determining the
isomorphism type of the maximal subgroups S<G of all 3-groups G with coclass
cc(G)=1, and establishing a general theorem on the connection between the
p-class towers of a number field F and of an unramified abelian p-extensions
E/F, we are able to provide a theoretical proof of the realization of certain
3-groups S with maximal class by 3-tower groups G(3,infinity,E) of dihedral
fields E with degree 6, which could not be realized up to now.

27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
16
The categories of this paper are: stat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics