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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1998 • Question 11

Question

Math 6310 • Algebra Fall 1998 • Question 11

Let \(p\) be a prime number, and let \(G\) be a finite group of order \(p^n\) acting on a set \(X\) consisting of \(r\) elements. Show that the number of points fixed by all elements of \(G\) is congruent to \(r\) modulo \(p\).

Raw LaTeX

Let \(p\) be a prime number, and let \(G\) be a finite group of order \(p^n\) acting on a set \(X\)
consisting of \(r\) elements. Show that the number of points fixed by all elements of \(G\) is
congruent to \(r\) modulo \(p\).

Topic Tags

Finite Group Theory Sylow Theorems p-Groups