The Notions of Center, Commutator and Inner Isomorphism for Groupoids

Ingeniería y Ciencia

Víctor Marín¹  Jesús Ávila¹ 

[1] Universidad del Tolima;

关键词: Groupoid;    normal subgroupoid;    normalizer;    center;    commutator;    inner isomorphisms;   

DOI  :  10.17230/ingciencia.16.31.1

来源: DOAJ

【 摘 要 】

In this paper we introduce some algebraic properties of subgroupoids and normal subgroupoids. we define other things, we define the normalizer of a wide subgroupoid H of a groupoid G and show that, as in the case of groups, this normalizer is the greatest wide subgroupoid of G in which H is normal. Furthermore, we provide definitions of the center Z(G) and the commutator G' of the groupoid G and prove that both of them are normal subgroupoids. We give the notions of inner and partial isomorphism of G and show that the groupoid I(G) given by the set of all the inner isomorphisms of G is a normal subgroupoid of A(G), the set of all the partial isomorphisms of G. Moreover, we prove that I(G) is isomorphic to the quotient groupoid G/Z(G), which extends to groupoids the corresponding well-known result for groups.

【 授权许可】

Unknown