3 papers
math.CO2024
Proving the 5-Engel identity in the 2-generator group of exponent four
Colin Ramsay
It is known that the fifth Engel word is trivial in the 2-generator group of exponent four , and so can be written as a product of fourth powers. Explicit products of…
math.CO2017
Listing Words in Free Groups
Colin Ramsay
Lists of equivalence classes of words under rotation or rotation plus reversal (i.e., necklaces and bracelets) have many uses, and efficient algorithms for generating these lists e…
math.GR2015
Writing Commutators of Commutators as Products of Cubes
Colin Ramsay
It is known that commutators of commutators can be written as products of cubes, with the current upper bound on the number of cubes being 60. We discuss how proofs extracted via c…