- #1
Kate2010
- 146
- 0
Homework Statement
I have to use the first isomorphism theorem to determine whether C16 (cyclic group order 16) has a quotient group isomorphic to C4.
Homework Equations
First isomorphism theorem
The Attempt at a Solution
C16 = {e, a, ..., a^15}
C4 = {e, b, ..., b^3}
Homomorphism f(a^m) = b^m 0<= m < 16
ker f is all x in C16 such that f(x) = e = b^4 = b^8 = b^12 = {e, a^4, a^8, a^12}
im f = {e, b^2, ..., b^15} = {e, b^2, b^3, b,..., b^3} = C4
Therefore, there is an isomorphism.
I'm unsure about my method here, especially finding I am f, as it initally appears that I am f is bigger than C4.