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February 7th, 2012, 10:56 PM  #1 
Senior Member Joined: Sep 2010 From: Germany Posts: 153 Thanks: 0  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??? 
February 8th, 2012, 12:54 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  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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