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2d edition affects no variable Akademie der Wissenschaften Burnside Burnside's paper Cambridge Philosophical Society coefficient conditions of Lemma constituent of G0 contain transitive Abelian contains a transitive da.b degree k2 dissertation Doctor of Philosophy equals zero equation Finite Order follows from Lemma G is imprimitive group characteristics group G group of degree group of prime Groups of Finite imprimitive and compound includes at least integer invariant least one letter left-hand member Lemma XIII Lemma XIV Lemma XV matrices of F matrix groups member of 6.2 mod qb multiple of q obtain permutation of order positive integers Preussischen Akademie prime degree proper subgroup proved relatively prime root of unity rows and columns Schur simply transitive group simply transitive permutation simply transitive primitive Sitzungsberichte der Preussischen solvable group stituent subgroup of degree subgroup of G subgroup of order substitution Theorie der einfach Theory of Groups transitive Abelian subgroup transitive permutation group