Generalizations of Lagrange and Sylow Theorems for Groupoids

TL;DR

This paper extends classical group theory theorems to finite groupoids, providing a classification method, and generalizations of Lagrange's and Sylow's theorems, linking coset cardinality and index.

Contribution

It introduces a novel classification approach for finite groupoids and generalizes fundamental theorems from group theory to the broader context of groupoids.

Findings

A classification method for finite groupoids

A generalized Lagrange's Theorem for groupoids

A Sylow theory applicable to groupoids

Abstract

We show a classification method for finite groupoids and discuss the cardinality of cosets and its relation with the index. We prove a generalization of the Lagrange's Theorem and establish a Sylow theory for groupoids.