Homomorphism
(Monday, May 3, 2010)
Definition
A mapping f: G ® G', where áG, *ñ and áG', °ñ are groups is called homomorphism if for each a, b e G, we have
f(a*b) = f(a)°f(b)
Note:
1. If G'=G, i.e., homomorphism of a group G to
itself is called endomorphism.
Note:
2. If f is onto, then f is said to be an
epimorphism.
3. If f is one-one and onto the f is said to
be an isomorphism.
4. If G' = G and f is one-one and onto, the f
is called an automorphism
Posted in Posted by waytofeed at 7:42 AM
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