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10 Nov 2019
Homorphisms
Let r D20 be an element of order n and let s D20 be a reflection. Suppose that phi: D20 -> D20 is a homomorphism such that phi(r) = r12. Prove that phi(s) is a reflection. Find all elements in the kernel Ker phi of phi. Prove that the factor group D20/Ker phi is nonabelian. Prove that D2o/ker phi is isomorphic to a dihedral group Dm. (What is m?)
Homorphisms
Let r D20 be an element of order n and let s D20 be a reflection. Suppose that phi: D20 -> D20 is a homomorphism such that phi(r) = r12. Prove that phi(s) is a reflection. Find all elements in the kernel Ker phi of phi. Prove that the factor group D20/Ker phi is nonabelian. Prove that D2o/ker phi is isomorphic to a dihedral group Dm. (What is m?)