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
Attachments
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.
$2.19