Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Polycyclic Presentation for the q-Tensor Square of a Polycyclic Group   Let $G$ be a group and $q$ a non-negative integer. We denote by $\nu^q(G)$ a
certain extension of the $q$-tensor square $G \otimes^q G$ by $G \times G$. In
this paper we derive a polycyclic presentation for $G \otimes^q G$, when $G$ is
polycyclic, via its embedding into $\nu^q(G)$. Furthermore, we derive
presentations for the $q$-exterior square $G \wedge^q G$ and for the second
homology group $H_2(G, \mathbb{Z}_q).$ Additionally, we establish a criterion
for computing the $q-$exterior centre $Z_q^\wedge (G)$ of a polycyclic group
$G, $ which is helpful for deciding whether $G$ is capable modulo $q$. These
results extend to all $q \geq 0$ existing methods due to Eick and Nickel for
the case $q = 0$.

14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
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
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics