Abelian Group or Commutative Group
"A group (G,O) is said to be an abelian group or a commutative group if (a O b) = (b O a) a, b ᗴ G . " OR "A non-empty set 'G' together with a binary operation 'O' is said to be a group, if the following laws holds for all the operations 'O'." Group holds the following given five laws : (a) Clouser Law : 'G' is cloused under the binary operation 'O' that is ( a O b ) = ( b O a ) ∀ a, b ᗴ G . (b) Associative Law : The associative law for the operation holds that is a O ( b O c ) = ( a O b ) O c ∀ a, b, c ᗴ G. (c) Existence of Identity Element : The identity element exists in 'G' that is there exists an element e ᗴ G such that a ᗴ e = e ᗴ a = a ∀ a ᗴ G. (d) Existence of Inverse Element : The inverse element of all the elements of 'G' exists that is for every a ᗴ G there exists an element b ᗴ G su...