Math 4107, exam 1September 22, 2009Each question is worth 20 points.1.Define the following terms.a. Normal subgroup.b. Homomorphism.c. Innerautomorphism.2.List all the elements of order 2 from the groupS4.3.Find integerskandℓ, satisfying55k+ 21ℓ= 1,|k| ≤20,|ℓ| ≤54.Don’t just write down the answer.Work it using the Euclidean algorithm(e.g. Knuth’s algorithm), so that I know you know some good mathematics.4.Consider the set of all 2×2 matrices of the formbracketleftBigg
This is the end of the preview.
access the rest of the document.