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Last modified on 25 July 2010, at 02:01
Abstract Algebra/Group Theory/Homomorphism/Homomorphism Maps Identity to Identity
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Abstract Algebra

Group Theory

Homomorphism
Theorem
Edit
Let
f
be a homomorphism from group
G
to group
K
.
Let
e
_{G}
and
e
_{K}
be identities of
G
and
K
.
f
(
e
_{G}
) =
e
_{K}
Proof
Edit
0.
f
maps to K
1.
inverse in K
.
2.
f
is a homomorphism
3.
identity
e
_{G}
.
4.
1.
.
5.
identity
e
_{K}
, definition of inverse
6.
identity
e
_{K}