On Burnside Theory for groupoids
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BULLETIN MATHÉMATIQUE de la Société des Sciences Mathématiques de Roumanie (Bull. Math. Soc. Sci. Math. Roumanie)
Fecha
2023Resumen
We explore the concept of conjugation between subgroupoids, providing several characteriza- tions of the conjugacy relation (Theorem A in §1.2). We show that two finite groupoid-sets, over a locally strongly finite groupoid, are isomorphic, if and only if, they have the same number of fixed points with respect to any subgroupoid with a single object (Theorem B in §1.2). Lastly, we examine the ghost map of a finite groupoid and the idempotents elements of its Burnside algebra. The exposition includes an Appendix where we gather the main general technical notions that are needed along the paper.