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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1999 • Question 3

Question

Math 6310 • Algebra Fall 1999 • Question 3

Let \(G\) be a group of order 55 acting on a set \(X\) consisting of 24 elements. Show that there is at least one element fixed by every element of \(G\).

Raw LaTeX

Let \(G\) be a group of order 55 acting on a set \(X\) consisting of 24 elements. Show that there is
at least one element fixed by every element of \(G\).

Topic Tags

Finite Group Theory Sylow Theorems