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This paper is concerned with the many deep and far reaching consequences of Ash’s positive solution of the type II conjecture for finite monoids. After rewieving the statement and history of the problem, we show how it can be used to decide if a finite monoid is in the variety generated by the Malcev product of a given variety and the variety of groups.… (More)

- Karsten Henckell, John L. Rhodes, Benjamin Steinberg
- IJAC
- 2010

We prove that if π is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are π-groups. In particular, when π is the empty set, we obtain Henckell’s decidability of aperiodic pointlikes. Our proof, restricted to the case of aperiodic semigroups, is simpler than the original proof.

- Karsten Henckell
- 1999

In this paper we give a new proof of the following result of Straubing and Thérien: every J -trivial monoid is a quotient of an ordered monoid satisfying the identity x ≤ 1. We will assume in this paper that the reader has a basic background in finite semigroup theory (in particular, Green’s relations and identities defining varieties) and in computer… (More)

- Karsten Henckell
- IJAC
- 2004

- Karsten Henckell
- IJAC
- 2010

Herein we generalize the holonomy theorem for finite semigroups (see [7]) to arbitrary semigroups, S, by embedding s^ into an infinite Zeiger wreath product, which is then expanded to an infinite iterative matrix semigroup. If S is not finite-J-above (where finite-J-above means every element has only a finite number of divisors), then S is replaced by g3,… (More)

- Karsten Henckell, John L. Rhodes, Benjamin Steinberg
- IJAC
- 2010

We give a short proof, using profinite techniques, that idempotent pointlikes, stable pairs and triples are decidable for the pseudovariety of aperiodic monoids. Stable pairs are also described for the pseudovariety of all finite monoids.

...................................................................................................................... vi CHAPTER 1: INTRODUCTION ........................................................................................1 Categorization… (More)

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