A partial-group framework encodes symmetries of individual components of disconnected figures, with semidirect product decompositions for two-component and lattice-translate figures.
Semidirect Products and Wreath Products of Localities
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abstract
We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidirect products of groups.
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Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins
A partial-group framework encodes symmetries of individual components of disconnected figures, with semidirect product decompositions for two-component and lattice-translate figures.