Geodesic
Invariants for metabelian groups of prime power exponent, colorings, and stairs
Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 267-297

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DOI

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 $R(2,n)$.
DOI : 10.4153/S0008414X21000675
Mots-clés : Burnside groups, metabelian groups, winding invariant, colorings, identities 
Barmak, Jonathan Ariel. Invariants for metabelian groups of prime power exponent, colorings, and stairs. Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 267-297. doi: 10.4153/S0008414X21000675
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