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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2004 • Question 4

Question

Math 6310 • Algebra Fall 2004 • Question 4

Let \(R\) be a commutative ring with identity. Let \(G\) be a finite subgroup of \(R^\times \), the group of units of \(R\). Prove that if \(R\) is an integral domain, then \(G\) is cyclic.

Raw LaTeX

Let \(R\) be a commutative ring with identity. Let \(G\) be a finite subgroup of \(R^\times\), the
group of units of \(R\). Prove that if \(R\) is an integral domain, then \(G\) is cyclic.

Topic Tags

Finite Group Theory Ideals and Quotient Rings Integral Closure Normal Subgroups and Commutator Subgroups