Corpus ID: 119595541

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}
}
  • A. Egri-Nagy, Chrystopher L. Nehaniv
  • Published 2013
  • Mathematics
  • arXiv: Group Theory
  • 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

    Figures from this paper.

    Decomposition of groups and the wreath product of permutation groups
    • N. Ghadbane
    • 2020
    Computational Holonomy Decomposition of Transformation Semigroups
    7
    On groups generated by involutions of a semigroup
    3
    Finite Computational Structures and Implementations: Semigroups and Morphic Relations
    3
    Finite Computational Structures and Implementations
    2
    Transformation Semigroups and State Machines

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 13 REFERENCES
    Practical Decomposition of Automata
    5
    The q-theory of Finite Semigroups
    241
    Self-Similar Groups
    330
    Permutation Groups
    280
    SgpDec – software package for hierarchical decompositions and coordinate systems, Version 0.7+
    • 2013
    ALGEBRAIC THEORY OF FINITE AUTOMATA NETWORKS
    22
    Cascade Decomposition of Arbitrary Semigroups
    4
    Generalized Wreath Products of Permutation Groups
    45
    Grigorchuk , and Zoran Šunić
    • 2003