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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1997 • Question 1

Question

Math 6310 • Algebra Fall 1997 • Question 1

Let \(G\) be a finite group with the property that for each positive integer \(n\), there are at most 2 subgroups of order \(n\) in \(G\). Prove that \(G\) is cyclic.

Raw LaTeX

Let \(G\) be a finite group with the property that for each positive integer \(n\), there are at most
2 subgroups of order \(n\) in \(G\). Prove that \(G\) is cyclic.

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups