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Topic: need help in abstract algebra
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hungli@texas.net

Posts: 7
Registered: 12/6/04
need help in abstract algebra
Posted: Oct 15, 1996 3:27 AM
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1. prove that if Z(G) is the center of G, then Z(G) is a normal
subgroup of G.

2. If G is a group and N is a normal subgroup of G , such that G/N is
abelian, prove that aba^-1b^-1 belong to N for all a, b belong to G.
(a^-1 mean a inverse same as b^-1)

3. Let G be a group, H a subgroup of G, and N is a normal subgroup of
G. Let the set HN = {hn | h belong to H, n belong to N}. Prove that :

(a) H intersect N is a normal subgroup of H.
(b) HN is a subgroup or G.
(c) N is a subgroup of HN and N is a normal subgroup of HN.
(HN) / N and H / (H intersection N) are isomorphic






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