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Let G be a group and let H1 and H2 be subgroups of G. Suppose that...

Let G be a group and let H1 and H2 be subgroups of G.

Suppose that G is finite and H1 and H2 have orders p and q, respectively, where p and q are distinct primes. Prove that H1 ∩ H2 = {e}.

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Answer #1

Here G be a group and H1 and H2 be sub group of G.

since H1 and H2 have orders p ,and q respectively so let H1=〈a〉 and H2=〈b〉

then ap =e and bq=e. (as every group of prime order is cyclic)

again let H1H2=

and we know that

from this formula we have seen that = either 1 or pq so when =pq

then we have that H1H2 =

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