Algorithmic Problems for Amalgams of Finite Semigroups

Algorithmic Problems in Amalgams of Finite Groups

Geometric methods proposed by Stallings [53] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [4, 25, 37, 38, 43, 48, 56]. It turns out that Stallings’ methods can be effectively generalized for the class of amalgams of finite groups [39]. In the present paper we employ subgroup gr...

Algorithmic Problems in Amalgams of Finite Groups: Conjugacy and Intersection

Geometric methods proposed by Stallings [46] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [3, 19, 29, 30, 36, 41, 49]. In the present paper we employ the generalized Stallings’ methods, developed by the author in [32], to solve various algorithmic problems concerning finitely g...

Amalgams of Free Inverse Semigroups

We study inverse semigroup amalgams of the form S U T where S and T are free inverse semigroups and U is an arbitrary nitely generated inverse subsemigroup of S and T. We make use of recent work of Bennett to show that the word problem is decidable for any such amalgam. This is in contrast to the general situation for semigroup amalgams, where recent work of Birget, Margolis and Meakin shows th...

Algorithmic Problems in Groups Semigroups and Inverse Semigroups

A Note on Amalgams of Inverse Semigroups