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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1995 • Question 3

Question

Math 6310 • Algebra Fall 1995 • Question 3

Suppose \(G\) is a finite simple group such that \(G\) has exactly 5 distinct Sylow \(p\)-subgroups for some prime \(p\). Prove that \(G\) is isomorphic to \(A_5\), the alternating group of order 60.

Raw LaTeX

Suppose \(G\) is a finite simple group such that \(G\) has exactly 5 distinct Sylow \(p\)-subgroups for
some prime \(p\). Prove that \(G\) is isomorphic to \(A_5\), the alternating group of order 60.

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups Sylow Theorems Symmetric and Alternating Groups