SgpDec

Hierarchical Composition and Decomposition of Permutation Groups and Transformation Semigroups

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A lot is going on around SgpDec. Following the upcoming GAP 4.7 a completely rewritten SgpDec will also be released. More detailed news.
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Related papers, drafts
Lagrange decomposition
Simple composition examples
On the Skeleton of a Transformation Semigroup

Holonomy decomposition of a small automaton (cascaded automaton, tiling picture, original automaton):