If H and K is subgroup of G and |H|=10,|K|=49 then how do you find |HnnK| ?

1 Answer
Feb 22, 2018

abs(H nn K) = 1

Explanation:

The order of any element of a group must be a divisor of the order of that group.

Given:

abs(H) = 10

we can deduce that any element of H has order 1, 2, 5 or 10.

Given:

abs(K) = 49

we can deduce that any element of K has order 1, 7 or 49

So any element of H nn K has order in { 1, 2, 5 } nn { 1, 7, 49 } = { 1 }.

That is: the only element of H nn K is the identity.