On the word problem for the free Burnside semigroups satisfying x 2 = x 3
A. N. Plyushchenko · Russian Mathematics · 2011
We study the word problem for the free Burnside semigroups satisfying x 2 = x 3. For any k > 2, we reduce this problem for the k-generated free Burnside semigroup B(2, 1, k) to the word problem for the two-generated semigroup B(2, 1, 2). Furthermore, if every element of B(2, 1, 2) is a regular language, then every element of B(2, 1, k) appears to be a regular language as well. Thus, Brzozowski’s conjecture holds for the semigroup B(2, 1, k) if and only if it holds for B(2, 1, 2).