Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of ergodic automorphisms in ergodic ${\mathbb Z}
  ^d$-actions on compact groups   Let $K$ be a compact metrizable group and $\Ga$ be a finitely generated group
of commuting automorphisms of $K$. We show that ergodicity of $\Ga$ implies
$\Ga$ contains ergodic automorphisms if center of the action, $Z(\Ga) = \{\ap
\in {\rm Aut}(K) \mid \ap {\rm commutes with elements of \rm} \Ga \}$ has DCC.
To explain that the condition on the center of the action is not restrictive,
we discuss certain abelian groups which in particular, retrieves Theorems of
Berend \cite{Be} and Schmidt \cite{Sc1} proved in this context.

13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int