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Author: lenis2000

graduate/docs/algebra-general-exam-syllabus.html

@@ -94,7 +94,7 @@ <h2 id="section-groups">I. Groups</h2>
 
     <div class="topic-category" role="heading" aria-level="3">Standard material.</div>
     <div class="topic-content">
-      <p>Group actions, orbits and stabilizers. Regular action and action on cosets; Cayley's theorem. Conjugation action: conjugacy classes, centralizers and normalizers. Class equation. Finite p-groups and their properties. Sylow theorems: proof and applications. Direct and semi-direct products. Groups of permutations: conjugacy in S<sub>n</sub>/A<sub>n</sub> and the simplicity of A<sub>n</sub> for n ≥ 5. Solvable and nilpotent groups. Free groups.</p>
+      <p>Group actions, orbits and stabilizers. Regular action and action on cosets; Cayley's theorem. Conjugation action: conjugacy classes, centralizers and normalizers. Class equation. Finite p-groups and their properties. Sylow theorems: proof and applications. Direct and semi-direct products. Groups of permutations: conjugacy in S<sub>n</sub>/A<sub>n</sub> and the simplicity of A<sub>n</sub> for n &ge; 5. Solvable and nilpotent groups. Free groups.</p>
     </div>
 
     <div class="topic-category" role="heading" aria-level="3">Additional topics.</div>