Algorithmic problems for finite groups and finite 0-simple 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...

Finite Permutation Groups and Finite Simple Groups

In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...

Finite Semigroups: Jewels and Problems

Algorithmic Problems in Groups Semigroups and Inverse Semigroups

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...