Year: 2013
Type: preprint
Abstract: Motivated by computational efficiency in algebraic automata theory here we define the cascade product of permutation groups as an external product, as a generic extension. It is the most general hierarchical product that uses arbitrary total functions to combine a linearly ordered set of permutation groups. Algebraically speaking, cascade products are explicitly constructed substructures of the iterated wreath product. We show how direct, semidirect and wreath products can be described as cascade products and we also discuss examples of composite groups that can only be constructed exactly as generic extensions by cascade products. The cascade construction naturally generalizes to the transformation semigroup case by leaving out the details of defining inverse operations.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
OpenAlex ID: W2117397007