- #1
hsong9
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Homework Statement
Show that there are exactly two homomorphisms f:C_(6) --> C_(4)
Homework Equations
Theorem.
let f: G -> G1 and h: G -> G1 be homomorphisms and assume that G=<X> is generaed by a subset X. Then f = h if and only if f(x) = h(x) for all x in X.
The Attempt at a Solution
C6 = <g>, |g| = 6. The divisors of 6 are 1,2,3,6
C4 = <g'>, |g'| = 4, the divisors of 4 are 1,2,4
only 1 and 2 of C6 are the divisors of C4.
so there are exactly two homomorphism.
right?