1. Mathematics
2. Algebra
3. Group Theory
4. 30330

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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)}.