मान लीजिए 'a' किसी समूह का एक अवयव है और O(a) = 30 है। तो O(a18) किसके बराबर है?

Let G be a cyclic group of order 6. Then, the number of elements g ∈ G such that G = ⟨g⟩ is:

A non-commutative (abelian) group has at least how many elements?

Consider the set G = {a + b√2 : a, b ∈ Q, the set of all rational numbers} with respect to the binary operation of usual addition. Which property fails to hold for G to be a non-abelian group?