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

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Answer 1 · 2018-02-22T07:13:53

$abs(H nn K) = 1$

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.

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