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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2016 • Question 3

Question

Math 6310 • Algebra Summer 2016 • Question 3

Let \(p\) be a prime integer, and \(G\) a group in which \(g^p\) is the identity for each \(g\) in \(G\). Show that \(G\) must be abelian if \(p=2\). Give an example where \(G\) is not abelian.

Raw LaTeX

Let \(p\) be a prime integer, and \(G\) a group in which \(g^p\) is the identity for each \(g\) in \(G\).
Show that \(G\) must be abelian if \(p=2\). Give an example where \(G\) is not abelian.

Topic Tags

Abelian Groups and Classification of Finite Abelian Groups Abelian Groups and Direct Sum Decompositions