Invariants for metabelian groups of prime power exponent, colorings, and stairs

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)′→Zn that we construct from colorings of the squares in the integer grid R×Z∪Z×R . In particular, we improve bounds found by Newman for the order of M(2,2k) . 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) .