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 $Latex ^ {-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.]
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