On Frobenius' Conjecture |
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Contents
PROPERTIES OF GROUPS HAVING A SMALL | 15 |
PROPERTIES OF A MINIMAL PAIR | 58 |
TECHNICAL RESULTS | 64 |
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Common terms and phrases
2-power 2ªis assume Burnside's theorem C(x₁ conclude Conjecture is true conjugate contain H contradiction cycle structure d₁ d₂ denote distinct double coset element of H elements of order equation finite group follows that Q Frobenius Furthermore G contains elements G is simple group G H₁ H₂ Hence integer dividing G involutions k₁ Ka(G kisidi Kpa(G Lemma Let G M₂ G M₂(G M₂a(G Ma(G minimal pair N(H₁ N(H₂ NG(H normal subgroup normal Sylow 2-subgroup number of elements number of subgroups occur Op(G p a prime p-group P₁ pa-l pa+1 particular permutation representation Proof PROPOSITION Q₁ Q₂ Qp+1 R₁ R₂ remark s₁ S₂ simple group simplicity of G solvable groups subgroup of G subgroup of index subgroups of order Suppose Syl G Syl₂(G Sylow p-subgroups Sylow's theorem Sylp x₁ xpa-b ոլ ոչ տլոլ