let H be a normal subgroup of G and let a belong to G . if the element aH has order 3 in the group G/H and |H|=10, what are the possibilities for the order of a?

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Q: (a) Prove that if K is a subgroup of G and L is a subgroup of H, then K x L is a subgroup of G x H.

A: The detailed solution of (a) is as follows below:

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