Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-abelian tensor square and related constructions of $p$-groups   Let $G$ be a group. We denote by $\nu(G)$ a certain extension of the
non-abelian tensor square $[G,G^{\varphi}]$ by $G \times G$. We prove that if
$G$ is a finite potent $p$-group, then $[G,G^{\varphi}]$ and the $k$-th term of
the lower central series $\gamma_k(\nu(G))$ are potently embedded in $\nu(G)$
(Theorem A). Moreover, we show that if $G$ is a potent $p$-group, then the
exponent $\exp(\nu(G))$ divides $p \cdot \exp(G)$ (Theorem B). We also study
the weak commutativity construction of powerful $p$-groups (Theorem C).

28
The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an