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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2008 • Question 2

Question

Math 6310 • Algebra Fall 2008 • Question 2

Let \(p\) be a prime integer. Let \(G\) be a finite \(p\)-group, with identity \(e\), and center \(Z\). If \(N\ne \{e\}\) is a normal subgroup of \(G\), prove that \(N\cap Z\ne \{e\}\).

Raw LaTeX

Let \(p\) be a prime integer. Let \(G\) be a finite \(p\)-group, with identity \(e\), and center \(Z\).
If \(N\ne \{e\}\) is a normal subgroup of \(G\), prove that \(N\cap Z\ne \{e\}\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups p-Groups