2019/09/11 by Carmelo Vaccaro, Vaccaro, Carmelo
Computer Science · Mathematics · #20E05 #20M05 #68R15 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1909.04863
openalex publication_date 2019/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The cyclically reduced product of two words u, v, denoted u * v, is the cyclically reduced form of the concatenation of u by v. This product is not associative. Recently S. V. Ivanov has proved that the Andrews-Curtis conjecture can be restated in terms of the cyclically reduced product and cyclic permutations instead of the reduced product and conjugations. In a previous paper we have started a thorough study of * and of the structure of the set of cyclically reduced words F(X) equipped with *. In particular we have found that a certain number of properties of the free group equipped with the reduced product can be generalized to (F(X), *). In this paper we continue this study by proving that a generalized version of the associative property holds for * in a special case. In a following paper we will prove that a more general version of the associative property holds for any case.