SgpDec: Cascade (De)Compositions of Finite Transformation Semigroups and Permutation Groups
Attila Egri-Nagy, James D. Mitchell, Chrystopher L. Nehaniv
TL;DR
The paper introduces SgpDec, a computer algebra package that enables hierarchical composition and decomposition of permutation groups and transformation semigroups using cascade products, facilitating structural analysis.
Contribution
It presents a novel method for hierarchical decomposition of algebraic structures via cascade products, implemented in the SgpDec package.
Findings
Efficient hierarchical decomposition of permutation groups.
Construction of substructures of wreath products.
Enhanced structural analysis capabilities.
Abstract
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.
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Taxonomy
Topicssemigroups and automata theory · Geometric and Algebraic Topology · Rings, Modules, and Algebras