Groupoids: Direct Products, Semidirect Products and Solvability
Algebra and discrete mathematics(2022)
摘要
We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Finally the notion of solvable groupoid is introduced and studied, in particular it is shown that a finite groupoid G is solvable if and only if its isotropy groups are.
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关键词
groupoid,direct product,product,semidirect product,solvable , 
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