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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2001 • Question 1

Question

Math 6310 • Algebra Fall 2001 • Question 1

Let \(G\) be a finite group, and let \(H\) be a subgroup of index \(p\), where \(p\) is the smallest prime number dividing the order of \(G\). Show that \(H\) is a normal subgroup of \(G\).

Raw LaTeX

Let \(G\) be a finite group, and let \(H\) be a subgroup of index \(p\), where \(p\) is the smallest
prime number dividing the order of \(G\). Show that \(H\) is a normal subgroup of \(G\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups