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February 7th, 2012, 10:56 PM   #1
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prove that Ax(e) is a subgroup of AxB

Can someone explain to me how to do the following?
Prove that is a subgroup of
I know that we should apply the subgroup criterion but what elements does have???
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February 8th, 2012, 12:54 PM   #2
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Re: prove that Ax(e) is a subgroup of AxB

The elements of A x {e} are {a, e} where a is an element of A and e is the identity element of B. So if A is Z_3 and B is Z_7, A x {e} is
{(0, 1), (1, 1), (2, 1)}
since 1 is the identity in Z_7 and the elements of Z_3 are 0, 1, and 2.
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