# Cascade Product of Permutation Groups

@article{EgriNagy2013CascadePO, title={Cascade Product of Permutation Groups}, author={A. Egri-Nagy and Chrystopher L. Nehaniv}, journal={arXiv: Group Theory}, year={2013} }

We define the cascade product of permutation groups as an external product, an explicit construction of substructures of the iterated wreath product that are much smaller than the full wreath product. This construction is essential for computational implementations of algebraic hierarchical decompositions of finite automata. We show how direct, semidirect, and wreath products and group extensions can all be expressed as cascade products, and analyse examples of groups that can be constructed… CONTINUE READING

7 Citations

SgpDec: Cascade (De)Compositions of Finite Transformation Semigroups and Permutation Groups

- Mathematics, Computer Science
- 2014

12

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