Let G be a group and let G=HxK. Give an example where J is a subgroup of G, but not of the form H_1xK_1 where H_1 is a subgroup of H and K_1 is a subgroup of K.

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- Dec 16th 2009, 06:42 PMpleasehelpme1Group and Direct Products
Let G be a group and let G=HxK. Give an example where J is a subgroup of G, but not of the form H_1xK_1 where H_1 is a subgroup of H and K_1 is a subgroup of K.

- Dec 16th 2009, 07:21 PMtonio
- Dec 16th 2009, 07:47 PMpleasehelpme1???
what exactly do you mean by this? can you prove this for me? and what are the subgroup H_1 and K_1 in this case?

- Dec 16th 2009, 08:52 PMDrexel28
- Dec 17th 2009, 05:53 AMpleasehelpme1...
That H_1 and K_1 must either be Z_2 or {0}. However, then J=Z_2xZ_2 or {0}x{0} contradicting the definition of J?

- Dec 17th 2009, 08:03 AMpleasehelpme1..
and this is additive subgroups right?