# Group Definition

Memorize Trick for Group Definition

C.A.N. I. ?
C= Closure
A= Associative: (ab)c = a(bc)
N= Neutral element (e): ae=ea=a
I= Inverse: a $^ {-1}$ = e

If only 50% (C.A.)=> Semi-Group

If Semi-Group + Neutral = (C.A.N.) = MoNoid

Note: No Inverse => not a Group

Arthur Cayley (UK, 1821-1895): first gave an abstract definition of Group @1854 while being a lawyer for 14 yrs, couldn’t find a teaching job. His definition was ignored for 25 years until 1882 by Walter Van Dyck who gave the final Axiomatic definition of Abstract Group. ie above [C.A.N.I.]