SOLUTION OF THE MEMBERSHIP PROBLEM FOR CERTAIN RATIONAL SUBSETS OF ONE-RELATOR GROUPS WITH A SMALL CANCELLATION CONDITION

作者：Juhasz Arye^*

来源：International Journal of Algebra and Computation, 2012, 22(4): 1250027.

DOI：10.1142/S0218196712500270

• One-relator groups
• Magnus subsemigroups
• membership problem
• small cancellation theory
• word combinatorics

Let n %26gt;= 2 be a natural number, X = {x(1), . . . , x(n)} and let F be the free group, freely generated by X. Let R be a cyclically reduced word in F such that its symmetric closure R in F satisfies the small cancellation condition C%26apos;(1/5) %26 T(4). Let G be the group presented by %26lt; X vertical bar R %26gt;. A Magnus subsemigroup of G is any subsemigroup of G generated by at most 2n - 1 elements of {x(1), . . . , x(n), x(1)(-1), . . . , x(n)(-1)}. In this paper we solve the Membership Problem for rational subsets of G which are contained in a Magnus subsemigroup of G, provided that R satisfies certain combinatorial conditions. We use small cancellation theory with word combinatorics.

• 出版日期2012-6