SgpDec: Cascade (De)Compositions of Finite Transformation Semigroups and Permutation Groups
نویسندگان
چکیده
We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products. transformation semigroup, permutation group, wreath product, Krohn-Rhodes Theory
منابع مشابه
Groups That Together with Any Transformation Generate Regular Semigroups or Idempotent Generated Semigroups
Let a be a non-invertible transformation of a finite set and let G be a group of permutations on that same set. Then 〈G, a 〉 \G is a subsemigroup, consisting of all non-invertible transformations, in the semigroup generated by G and a. Likewise, the conjugates ag = g−1ag of a by elements g ∈ G generate a semigroup denoted 〈ag | g ∈ G〉. We classify the finite permutation groups G on a finite set...
متن کاملOn the Graphs Related to Green Relations of Finite Semigroups
In this paper we develop an analog of the notion of the con- jugacy graph of nite groups for the nite semigroups by considering the Green relations of a nite semigroup. More precisely, by de ning the new graphs $Gamma_{L}(S)$, $Gamma_{H}(S)$, $Gamma_{J}(S)$ and $Gamma_{D}(S)$ (we name them the Green graphs) related to the Green relations L R J H and D of a nite semigroup S , we first atte...
متن کاملPermutation groups and transformation semigroups
In collaboration with João Araújo and others, I have been thinking about relations between permutation groups and transformation semigroups. In particular, what properties of a permutation group G on a set Ω guarantee that, if f is any non-permutation on Ω (or perhaps any non-permutation of rank k), then the transformation semigroup 〈G, f〉 has specified properties. There is far too much to summ...
متن کاملRestricted cascade and wreath products of fuzzy finite switchboard state machines
A finite switchboard state machine is a specialized finite state machine. It is built by binding the concepts of switching state machines and commutative state machines. The main purpose of this paper is to give a specific algorithm for fuzzy finite switchboard state machine and also, investigates the concepts of switching relation, covering, restricted cascade products and wreath products of f...
متن کاملComputing finite semigroups
Using a variant of Schreier’s Theorem, and the theory of Green’s relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids...
متن کامل