Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On identities in the products of group varieties   Let ${\cal B}_n$ be the variety of groups satisfying the law $x^n=1$. It is
proved that for every sufficiently large prime $p$, say $p>10^{10}$, the
product ${\cal B}_p{\cal B}_p$ cannot be defined by a finite set of identities.
This solves the problem formulated by C.K. Gupta and A.N. Krasilnikov in 2003.
We also find the axiomatic and the basis ranks of the variety ${\cal B}_p{\cal
B}_p$. For this goal, we improve the estimate for the basis rank of the product
of group varieties obtained by G. Baumslag, B.H. Neumann, H. Neumann and P.M.
Neumann long ago.

12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol