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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2001 • Question 8

Question

Math 6310 • Algebra Fall 2001 • Question 8

Let \(G\) be a nonabelian group of order \(p^3\) for a prime \(p\) and and let \(Z\) be its center. Show that \(G/Z\cong \mathbb {Z}/p\mathbb {Z}\oplus \mathbb {Z}/p\mathbb {Z}\).

Raw LaTeX

Let \(G\) be a nonabelian group of order \(p^3\) for a prime \(p\) and and let \(Z\) be its center.
Show that \(G/Z\cong \mathbb{Z}/p\mathbb{Z}\oplus \mathbb{Z}/p\mathbb{Z}\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups Sylow Theorems p-Groups