Question

a * H = H * a relation holds if __________

(a) H is semigroup of an abelian group

(b) H is monoid of a group

(c) H is a cyclic group

(d) H is subgroup of an abelian group

I got this question in an interview for internship.

The above asked question is from Groups in division Groups of Discrete Mathematics

Answer 1

The correct option is (d) H is subgroup of an abelian group

For explanation: If h is the subgroup of an abelian group G, then the set of left cosets of H in G is to be set of right cosets i.e, a * H = H * a. Hence, subgroup is called the normal subgroup.