GR 9367 # 59

Two subgroups H and K of a group have orders 12 and 30, respectively. Which of the following could Not be the order of the subgroup of G generated by H and K?

answer: A 30

I couldn't figure it out.

Thank you very much in advance!

GR 9367 # 59

Two subgroups H and K of a group have orders 12 and 30, respectively. Which of the following could Not be the order of the subgroup of G generated by H and K?

answer: A 30

I couldn't figure it out.

Thank you very much in advance!

Two subgroups H and K of a group have orders 12 and 30, respectively. Which of the following could Not be the order of the subgroup of G generated by H and K?

answer: A 30

I couldn't figure it out.

Thank you very much in advance!

The subgroup H of order 12 is going to be a subgroup of the subgroup generated by H and K, so 12 must divide the order of this second subgroup. 12 doesn't divide 30.

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