Results 1 
5 of
5
Coherence, local quasiconvexity and the perimeter of 2complexes
, 2002
"... A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a map between two finite 2complexes which is introduced here. ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a map between two finite 2complexes which is introduced here. In the groups to which this theory applies, a presentation for a finitely generated subgroup can be computed in quadratic time relative to the sum of the lengths of the generators. For many of these groups we can show in addition that they are locally quasiconvex. As an application of these results we prove that onerelator groups with sufficient torsion are coherent and locally quasiconvex and we give an alternative proof of the coherence and local quasiconvexity of certain 3manifold groups. The main application is to establish the coherence
Normal Forms for Free Aperiodic Semigroups
 Int. J. Algebra Comput
, 1999
"... The implicit operation # is the unary operation which sends each element of a finite semigroup to the unique idempotent contained in the subsemigroup it generates. Using # there is a welldefined algebra which is known as the free aperiodic semigroup. In this article we show that for each n, the ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
The implicit operation # is the unary operation which sends each element of a finite semigroup to the unique idempotent contained in the subsemigroup it generates. Using # there is a welldefined algebra which is known as the free aperiodic semigroup. In this article we show that for each n, the n generated free aperiodic semigroup is defined by a finite list of pseudoidentities and has a decidable word problem. In the language of implicit operations, this shows that the pseudovariety of finite aperiodic semigroups is #recursive. This completes a crucial step towards showing that the KrohnRhodes complexity of every finite semigroup is decidable.
Maximal Groups in Free Burnside Semigroups
, 1998
"... . We prove that any maximal group in the free Burnside semigroup defined by the equation x n = x n+m for any n 1 and any m 1 is a free Burnside group satisfying x m = 1. We show that such group is free over a well described set of generators whose cardinality is the cyclomatic number of a gr ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. We prove that any maximal group in the free Burnside semigroup defined by the equation x n = x n+m for any n 1 and any m 1 is a free Burnside group satisfying x m = 1. We show that such group is free over a well described set of generators whose cardinality is the cyclomatic number of a graph associated to the J class containing the group. For n = 2 and for every m 2 we present examples with 2m \Gamma 1 generators. Hence, in these cases, we have infinite maximal groups for large enough m. This allows us to prove important properties of Burnside semigroups for the case n = 2, which was almost completely unknown until now. Surprisingly, the case n = 2 presents simultaneously the complexities of the cases n = 1 and n 3: the maximal groups are cyclic of order m for n 3 but they can have more generators and be infinite for n 2; there are exactly 2 jAj J classes and they are easily characterized for n = 1 but there are infinitely many J classes and they are difficult to c...