Question

If group G has 65 elements and it has two subgroups namely K and L with order 14 and 30. What can be order of K intersection L?

(a) 10

(b) 42

(c) 5

(d) 35

This question was posed to me by my college director while I was bunking the class.

This interesting question is from Groups in chapter Groups of Discrete Mathematics

Answer 1

Right choice is (c) 5

To explain I would say: As it is an intersection so the order must divide both K and L. Here 3, 6, 30 does not divide 14. But 5 must be the order of the group as it divides the order of intersection of K and L as well as the order of the group.