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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1996 • Question 1

Question

Math 6310 • Algebra Fall 1996 • Question 1

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

Raw LaTeX

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

Topic Tags

Finite Group Theory Sylow Theorems p-Groups