Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Erd\H{o}s-Ginzburg-Ziv inverse theorems for Dihedral and Dicyclic
  groups   Let $G$ be a finite group and exp$(G)$ = lcm$\{$ord$(g)$$\mid$$g \in G \}$. A
finite unordered sequence of terms from $G$, where repetition is allowed, is a
product-one sequence if its terms can be ordered such that their product equals
the identity element of $G$. We denote by $\mathsf s (G)$ (or $\mathsf E (G)$
respectively) the smallest integer $\ell$ such that every sequence of length at
least $\ell$ has a product-one subsequence of length $\exp (G)$ (or $|G|$
respectively). In this paper, we provide the exact values of $\mathsf s (G)$
and $\mathsf E (G)$ for Dihedral and Dicyclic groups and we provide explicit
characterizations of all sequences of length $\mathsf s (G) - 1$ (or $\mathsf E
(G) - 1$ respectively) having no product-one subsequence of length $\exp (G)$
(or $|G|$ respectively).

9
The categories of this paper are: nlin
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin