Question

A direct product of a group G possess which of the following characteristics?

(a) a multiplication of subgroups of G

(b) a factorization via subgroups of G

(c) a superset of subgroups of G

(d) a maximal power set of subgroups

I have been asked this question in an interview for internship.

My question comes from Graph’s Matrices in portion Graphs of Discrete Mathematics

Answer 1

Right option is (b) a factorization via subgroups of G

Explanation: A direct product of a group G is a factorization via subgroups of G when the intersection is nontrivial, say X and Y, such that G = XY, X intersect Y = 1, and [X, Y]=1 and X, Y are normal in G.