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DUE 1 MAY 2013
1. Let G be a group and H be a normal subgroup of G. Prove the universality property of the
quotient group G/H :
If f : G G is a group homomorphism such that H ker f, there exists a unique group
MATH 100C Final Exam Study Guide
First, let me warn you that this is by no means a complete list of problems, or topics. Just highlights.
The rst thing you should do when preparing for the exam is to go through your notes, the relevant section
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DUE 24 APRIL 2013
1. (a) Find the lattice of the subelds F of L = F316 that contain K = F32 .
(b) Determine which subelds F have the property that L/F is normal. Justify your answer.
(c) Determine which subelds F have the
DUE 17 APRIL 2013
1. Compute the Galois group G = Gal(F316 /F32 ) where Fq denotes the nite eld with q elements. Hint: Frobenius.
2. With the notation from the previous problem, nd all the subgroups of G.
3. With the notat