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UNIQUENESS THEOREMS Chapter 1 General Lemmas
Two Theorems on Doubly Transitive Groups
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2-central 2-group 2-transitive acts faithfully assertion assume Borel subgroup Burnside's Theorem centralizes Cg(x CG(z choose Ck(x class of involutions CM(x completes the proof component conclude conjugacy class conjugate Consequently contains a Sylow Corollary cosets Cx(u cyclic cyclic group definition dihedral dihedral group element field automorphism Finally following conditions hold following holds four-group four-subgroup Frattini argument Frobenius group G-conjugate Hence hypothesis implies induces an inner induces inner automorphisms interchanges invariant inverts isomorphic isomorphism type lies maximal subgroup Moreover NG(K Nj(B non-inner nonabelian noninner automorphism normal subgroup notation odd order odd prime p-component p-subgroup p'-group parabolic subgroup particular permutes preceding lemma preimage proof is complete proof of Proposition proof of Theorem prove Lemma quasisimple satisfies simple Bender group simple group solvable strongly closed subgroup of G Suppose false Sylow 2-subgroup t-invariant Table Theorem PUi Theorem ZD transitive unique whence