A class of group-like objects
نویسنده
چکیده
We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects. In the study of generalizing the Lie correspondence between linear Lie groups and linear Lie algebras, we have found a generalization of the notion of inverse in group theory. The generalization of the notion of inverse in group theory not only is indispensable in our method of generalizing the Lie correspondence between linear Lie groups and linear Lie algebras, but also plays a key role in our study of group-like, ring-like and field-like objects. In this paper, we use the generalization of the notion of inverse to introduce a class of group-like objects. The class of group-like objects share many properties with groups. The main result of this paper is that Cayley Theorem on groups has a counterpart in the class of group-like objects.
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