Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A reciprocity on finite abelian groups involving zero-sum sequences II   Let $G$ be a finite abelian group. For any positive integers $d$ and $m$, let
$\varphi_G(d)$ be the number of elements in $G$ of order $d$ and $\mathsf
M(G,m)$ be the set of all zero-sum sequences of length $m$. In this paper, for
any finite abelian group $H$, we prove that $$|\mathsf M(G,|H|)|=|\mathsf
M(H,|G|)|$$ if and only if $\varphi_G(d)=\varphi_H(d)$ for any $d|(|G|,|H|)$.
We also consider an extension of this result to non-abelian groups in terms of
invariant theory.

18
The categories of this paper are: econ
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex