Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distinguishing number of the direct product and wreath product
  action   Let G be a group acting faithfully on a set X. The distinguishing number of
the action of G on X is the smallest number of colors such that there exists a
coloring of X where no nontrivial group element induces a color-preserving
permutation of X. In this paper, we consider the distinguishing number of two
important product actions, the wreath product and the direct product. Given
groups G and H acting on sets X and Y respectively, we characterize the
distinguishing number of the wreath product of G and H in terms of the number
of distinguishing colorings of X with respect to G and the distinguishing
number of the action of H on Y. We also prove a recursive formula for the
distinguishing number of the action of the Cartesian product of two symmetric
groups S_m x S_n on [m] x [n].

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex