Understanding Burnside's Theorem
Expository, character-theoretic proof of Burnside's p^a q^b solvability theorem via Sylow theory, the class equation, column orthogonality, and algebraic-integer methods; key lemmas (|χ(g)| ≤ χ(1), conjugacy-class size criterion).
Overview
- Expository, character-theoretic proof of Burnside’s $p^a q^b$ theorem via: Sylow theory, the class equation, column orthogonality relations, and algebraic-integer methods.
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Proved supporting lemmas (e.g., $ \chi(g) \leq \chi(1)$ and a conjugacy-class size criterion) and deduced solvability of groups with $ G =p^aq^b$.