Question

A trivial subgroup consists of ___________

(a) Identity element

(b) Coset

(c) Inverse element

(d) Ring

I had been asked this question in a national level competition.

My query is from Groups topic in portion Groups of Discrete Mathematics

Answer 1

The correct option is (a) Identity element

To explain: Let G be a group under a binary operation * and a subset H of G is called a subgroup of G if H forms a group under the operation *. The trivial subgroup of any group is the subgroup consisting of only the Identity element.