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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2004 • Question 4

Question

Math 6310 • Algebra Spring 2004 • Question 4

Suppose \(H\) is a subgroup of the finite group \(G\) and the index of \(H\) in \(G\) is the smallest prime dividing the order of \(G\). Prove that \(H\) is a normal subgroup of \(G\).

Raw LaTeX

Suppose \(H\) is a subgroup of the finite group \(G\) and the index of \(H\) in \(G\) is the smallest
prime dividing the order of \(G\). Prove that \(H\) is a normal subgroup of \(G\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups