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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2013 • Question 2

Question

Math 6310 • Algebra Fall 2013 • Question 2

Let \(P\) be a \(p\)-Sylow subgroup of a group \(G\), and \(N\) a normal subgroup of \(G\). Prove that \(P\cap N\) is a \(p\)-Sylow subgroup of \(N\).

Raw LaTeX

Let \(P\) be a \(p\)-Sylow subgroup of a group \(G\), and \(N\) a normal subgroup of \(G\). Prove that
\(P\cap N\) is a \(p\)-Sylow subgroup of \(N\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups Sylow Theorems