Algebra - Group Theory Q&A in Tamil | TN TRB PG | CSIR NET | SET

Algebra - Group Theory Q&A | TN TRB PG | CSIR NET | SET.

Group

Definition : A non-empty set G is said to form a group if  in G there is defined a binary operation, called the product and denoted by (·) such that

1.    a, b ∈ G ⇒ a · b ∈ G (Closure axiom)

2.    a, b, c ∈ G ⇒ a · (b · c) = (a · b) · c (Associative axiom)

3.    There exists an element e ∈ G such that a · e = e · a = a, ∀ a ∈ G (Existence of  identity)

4.     ∀ a ∈ G there exists an element a⁻¹ ∈ G such that a·a⁻¹ = a⁻¹ ·a = e (Existence of inverse).

(Z, +) is an infinite abelian group.

Also (Q, +), (R , +), (C, +) are infinite abelian groups.