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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2009 • Question 3

Question

Math 6310 • Algebra Spring 2009 • Question 3

A group of order 81 acts on a set \(X\) with 30 elements. Show that some element of \(X\) is fixed by at least 27 elements. How many elements of \(X\) are fixed by precisely 3 elements, assuming there is at least one such element?

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A group of order 81 acts on a set \(X\) with 30 elements. Show that some element of \(X\) is fixed
by at least 27 elements. How many elements of \(X\) are fixed by precisely 3 elements, assuming
there is at least one such element?

Topic Tags

Finite Group Theory Sylow Theorems