THE SOLUTION TO THE WORD PROBLEM FOR THE RELATIVELY FREE SEMIGROUPS SATISFYING Ta = Ta+b WITH a ≥ 6
Jonathan P. McCammond · International Journal of Algebra and Computation · 1991
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.