# Direct product

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)}.

https://brainmass.com/math/group-theory/direct-product-groups-30330

#### Solution Preview

Please see the attachment.

Proof:

, are groups, . Let be the identity of group and be identity of group . Then , .

(a) Show that and are subgroups of ...

#### Solution Summary

This is a proof regarding subgroups.

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