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# Direct product

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Let G1 and G2 be groups, and let G be a direct product of G1 x G2.
Let H = {(x1, x2) element G1 x G2 | x2 = e} and let K = {(x1, x2) element G1 x G2| x1 = e}.

(a) Show that H and K are subgroups of G.
(b) Show that HK = KH = G
(c) Show that H [see attachment] K = {(e,e)}.

##### Solution Summary

This is a proof regarding subgroups.

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Proof:
, are groups, . Let be the identity of group and be identity of group . Then , .
(a) Show that and are subgroups of ...

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