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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
$R(2,n)$
.
MSC classification
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society, 2021
Footnotes
The author is supported by CONICET and partially supported by grants PICT-2017-2806, PIP 11220170100357CO, and UBACyT 20020160100081BA.
References
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