What is group - Definition and Meaning

Group :

A set of data which satisfies a few conditions or properties like closure, identity, associativity, and inverse can be called as a group.


Formula :

a,b,c ε (G,*), 1) Closure a*b ε G, 2) Associative (a*b)*c = a*(b*c), 3) Identity a*e = e*a = a, where e is identity element, and 4) Inverse a*a-1 = a-1*a = e

Example :

{1,2,3,...} ε (G,+), 1) Closure 1+2 = 3, 3 εG, 2) Associative (1+2)+3 = 1+(2+3) = 6, 3) Identity 1 + 0 = 0 + 1 = 1 where 0 is identity element of additive, and 4) Inverse 1 -1 = -1 + 1 = 0
Graph Greatest Common Factor (GCF)

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