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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2019 • Question 9

Question

Math 6310 • Algebra Fall 2019 • Question 9

Suppose \(\varphi :G\longrightarrow H\) is a group homomorphism and \(H\) is a group of order 33. Further suppose that \(N\supseteq \ker \varphi \) is a subgroup of \(G\). Prove that \(N\) is normal.

Raw LaTeX

Suppose \(\varphi:G\longrightarrow H\) is a group homomorphism and \(H\) is a group of order 33.
Further suppose that \(N\supseteq\ker\varphi\) is a subgroup of \(G\). Prove that \(N\) is normal.

Topic Tags

Finite Group Theory Hom Functors and Module Homomorphisms Normal Subgroups and Commutator Subgroups Polynomial Rings and Ring Homomorphism Kernels