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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2003 • Question 7

Question

Math 6310 • Algebra Fall 2003 • Question 7

Suppose \(G\) is a group of order \(p^n\) where \(p\) is a prime and \(n>1\). If \(A\) is the group of all automorphisms of \(G\), prove that \(p\) divides the order of \(A\).

Raw LaTeX

Suppose \(G\) is a group of order \(p^n\) where \(p\) is a prime and \(n>1\). If \(A\) is the group of
all automorphisms of \(G\), prove that \(p\) divides the order of \(A\).

Topic Tags

Finite Group Theory Sylow Theorems p-Groups