Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremal product-one free sequences over $C_n \rtimes_s C_2$   Let $G$ be a finite group multiplicatively written. The small Davenport
constant of $G$ is the maximum positive integer ${\sf d}(G)$ such that there
exists a sequence $S$ of length ${\sf d}(G)$ for which every subsequence of $S$
is product-one free. Let $s^2 \equiv 1 \pmod n$, where $s \not\equiv \pm1 \pmod
n$. It has been proven that ${\sf d}(C_n \rtimes_s C_2) = n$ (see Lemma 6 of
[Zhuang, Gao; Europ. J. Combin. 26 (2005), 1053-1059]). In this paper, we
determine all sequences over $C_n \rtimes_s C_2$ of length $n$ which are
product-one free. It completes the classification of all product-one free
sequences over every group of the form $C_n \rtimes_s C_2$, including the
quasidihedral groups and the modular maximal-cyclic groups.

37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org