3 research outputs found
Invariants for metabelian groups of prime power exponent, colorings and stairs
We study the free metabelian group of prime power exponent on
two generators by means of invariants that we
construct from colorings of the squares in the integer grid . In particular we improve bounds
found by M.F. Newman for the order of . We study identities in
, which give information about identities in the Burnside group
and the restricted Burnside group .Comment: 29 pages, 16 figure
The 2-generator restricted burnside group of exponent 7
We report on our construction of a power-commutator presentation for R(2, 7), the largest finite 2-generator group of exponent 7. Our calculations show that R(2, 7) has order 720416, nilpotency class 28, and derived length 5. The calculations also imply that the associated Lie ring of R(2, 7) satisfies relations which are not consequences of the multilinear identities which hold in the associated Lie rings of groups of exponent 7