Question

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

Answer 1

`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.