Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hausdorff dimension in a family of self-similar groups   For each prime p and a monic polynomial f, invertible over p, we define a
group G_{p,f} of p-adic automorphisms of the p-ary rooted tree. The groups are
modeled after the first Grigorchuk group, which in this setting is the group
G_{2,x^2+x+1}. We show that the constructed groups are self-similar, regular
branch groups. This enables us to calculate the Hausdorff dimension of their
closures, providing concrete examples (not using random methods) of
topologically finitely generated closed subgroups of the group of p-adic
automorphisms with Hausdorff dimension arbitrarily close to 1. We provide a
characterization of finitely constrained groups in terms of the branching
property, and as a corollary conclude that all defined groups are finitely
constrained. In addition, we show that all infinite, finitely constrained
groups of p-adic automorphisms have positive and rational Hausdorff dimension
and we provide a general formula for Hausdorff dimension of finitely
constrained groups. Further ``finiteness'' properties are also discussed
(amenability, torsion and intermediate growth).

8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph