In this paper, all semigroups are assumed to be finite unless otherwise stated. If H is a pseudovariety of groups (that is, a class of groups closed under formation of finite direct products, subgroups and quotients groups), then it is natural to define a group to be Hsolvable if it has a subnormal series each of whose quotients belongs to H. For instance a group is solvable in the classical se...

We prove that the pseudovariety DS, of all nite monoids each of whose regular D-classes is a subsemigroup, is local. (A pseudovariety (or variety) V is local if any category whose local monoids belong to V divides a member of V). The proof uses the \kernel theorem" of the rst two authors together with the description by P. Weil of DS as an iterated \block product". The one-sided analogues of th...

We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of ...

We present an algorithm to compute the pointlike subsets of a finite semigroup with respect to the pseudovariety R of all finite R-trivial semigroups. The algorithm is inspired by Henckell’s algorithm for computing the pointlike subsets with respect to the pseudovariety of all finite aperiodic semigroups. We also give an algorithm to compute J-pointlike sets, where J denotes the pseudovariety o...

The notion of reducibility for a pseudovariety has been introduced as an abstract property which may be used to prove decidability results for various pseudovariety constructions. This paper is a survey of recent results establishing this and the stronger property of complete reducibility for specific pseudovarieties.

This paper determines all pseudovarieties of nite semigroups whose powers are contained in DA. As an application, it is shown that it is computable, for a decidable pseudovariety V of aperiodic semigroups, the least exponent n such that the iterated power P n V is the pseudovariety of all nite semigroups.

We call a pseudovariety finite join irreducible if V ≤ V1 ∨V2 =⇒ V ≤ V1 or V ≤ V2. We present a large class of group mapping semigroups generating finite join irreducible pseudovarieties. We show that many naturally occurring pseudovarieties are finite join irreducible including: S, DS, CR, CS and H, where H is a group pseudovariety containing a non-nilpotent group.

in present study, the kinetic parameters of purified trypsin from pyloric caeca of common kilka (c.cultriventris caspia) were measured using the amidolytic (bapna) and esterolytic (tame) substrates. the results of the kinetic comparison between bapna and tame substrates showed that kinetic parameters including maximum velocity (vmax), catalytic constant (kcat) and catalytic efficiency (kcat/km)...

We introduce a series of new polynomially computable implicit operations on the class of all finite semigroups. These new operations enable us to construct a finite pro-identity basis for the pseudovariety H of all finite semigroups whose subgroups belong to a given finitely based pseudovariety H of finite groups.