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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2004 • Question 10

Question

Math 6310 • Algebra Fall 2004 • Question 10

Let \(G\) be a finite group with identity \(e\). Suppose that for all \(a,b\in G\) distinct from \(e\), there exists an automorphism \(\tau \) of \(G\) such that \(\tau (a)=b\). Prove that \(G\) is abelian.

Raw LaTeX

Let \(G\) be a finite group with identity \(e\). Suppose that for all \(a,b\in G\) distinct from \(e\),
there exists an automorphism \(\tau\) of \(G\) such that \(\tau(a)=b\). Prove that \(G\) is abelian.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Finite Group Theory