The Solution to the Word Problem for the Relatively Free Semigroups Satisfying TA = Ta+b with a ≥ 6

In this article the word problem for certain Burnside semigroups is shown to be decidable. For each word W ∈ A* a nondeterministic, finite-state automaton is constructed. This automaton accepts a word iff it is equivalent to W under the relations Ta = Ta+b, where a and b are fixed positive integers and T is an arbitrary word in A*. The method decides the word problem for those cases where a ≥ 6. The maximal subgroups are shown to be cyclic groups of order b.