Abstract Algebra exercise 8 solution pdf. Groups. A non-empty set G is said to form a group with respect to binary composition o , if (i) G in closed under the composition, (ii) o is associative, (iii) there exists an element e in G such that aoe=eoa=e for all a in G. (iv) for each elementa in G, there exists an element a' in G such that a'oa=aoa'=e The group in denoted by the symbol (G.,o). The element e is said to be an identity element in the group. We shall prove that there is only one inverse element in the group and therefore e will be said to be the identity clement. The element a' is said to be an inverse of a .We shall prove that each element a has only one inverse and therefore a' will be said to be the inverse of a . Definition, A group (G,o) is said to be a commutative group or an the name of Norwegian mathematician N. Abel) if composition is commutative. Necessary Theorem: theorem 1. A group (G,o) contains only one identity element. Theorem 2. ...
Bah ☺ gd gd
ReplyDelete