Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2003 • Question 1

Question

Math 6310 • Algebra Fall 2003 • Question 1

Suppose \(H\) is a subgroup of the group \(G\) such that \(x^2\in H\) for all \(x\in G\). Prove that \(H\) is a normal subgroup of \(G\).

Raw LaTeX

Suppose \(H\) is a subgroup of the group \(G\) such that \(x^2\in H\) for all \(x\in G\). Prove that
\(H\) is a normal subgroup of \(G\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups