Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dp-minimal profinite groups and valuations on the integers   We study dp-minimal infinite profinite groups that are equipped with a
uniformly definable fundamental system of open subgroups. We show that these
groups have an open subgroup $A$ such that either $A$ is a direct product of
countably many copies of $\mathbb{F}_p$ for some prime $p$, or $A$ is of the
form $A \cong \prod_p \mathbb{Z}_p^{\alpha_p} \times A_p$ where $\alpha_p <
\omega$ and $A_p$ is a finite abelian $p$-group for each prime $p$. Moreover,
we show that if $A$ is of this form, then there is a fundamental system of open
subgroups such that the expansion of $A$ by this family of subgroups is
dp-minimal. Our main ingredient is a quantifier elimination result for a class
of valued abelian groups. We also apply it to $(\mathbb{Z},+)$ and we show that
if we expand $(\mathbb{Z},+)$ by any chain of subgroups $(B_i)_{i<\omega}$, we
obtain a dp-minimal structure. This structure is distal if and only if the size
of the quotients $B_i/B_{i+1}$ is bounded.

35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg