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Invariants for metabelian groups of prime power exponent, colorings, and stairs
Published online by Cambridge University Press: 10 December 2021
Abstract
We study the free metabelian group $M(2,n)$ of prime power exponent n on two generators by means of invariants $M(2,n)'\to \mathbb {Z}_n$ that we construct from colorings of the squares in the integer grid $\mathbb {R} \times \mathbb {Z} \cup \mathbb {Z} \times \mathbb {R}$ . In particular, we improve bounds found by Newman for the order of $M(2,2^k)$ . We study identities in $M(2,n)$ , which give information about identities in the Burnside group $B(2,n)$ and the restricted Burnside group $R(2,n)$ .
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- © Canadian Mathematical Society, 2021
Footnotes
The author is supported by CONICET and partially supported by grants PICT-2017-2806, PIP 11220170100357CO, and UBACyT 20020160100081BA.