Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New perspectives of the power-commutator-structure: Coclass trees of
  CF-groups and related BCF-groups   Let e>1 be an integer. Among the finite 3-groups G with bicyclic commutator
quotient G/G' ~ C(3^e) * C(3), having one non-elementary component with
logarithmic exponent e, there exists a unique pair of coclass trees with
distinguished rank distribution rho ~ (2,2,3;3). One tree T(e)(M(e,1)) consists
of CF-groups with coclass e, and the other tree T(e+1)(M(e+1,1)) consists of
BCF-groups with coclass e+1. It is proved that, due to a chain of periodic
bifurcations, the vertices of all pairs (T(e),T(e+1)) with e>2 can be
constructed as p-descendants of the single root M(3,1) of order 729 by means of
the p-group generation algorithm by Newman and O'Brien.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc