## On the theory of substitution groups and its application to algebraic equations |

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### Contents

Theory of substitutiongroups | 1 |

Lagranges Researches | 2 |

2 Elementary propositions on substitutions | 7 |

15 other sections not shown

### Common terms and phrases

Abelian equations according alternate group belongs binomial equations biquadratic equation called chain of Abelian circular substitution coefficients are rational conjugate values cubic equation cyclic subgroup denote different powers domain of rationality equations of prime expressible in terms factors of composition form a group four letters function of xlt Galois Galoisian equation given equation group G groups of operations H under G holoedrically isomorphic indeterminate quantities irreducible equation Jordan Kronecker Lagrange's theorem letters xlt metacyclic group Netto notations nth root OSKAR BOLZA permutation prime degree prime index prime numbers rational function rational quantities rationally expressible rationally known remains unaltered resolvent equation root of unity roots are rationally roots xlt Serret solution solvable by radicals subgroup H subgroup of G substi substitution-group substitutions of G substitutions of three substitutions which leave supposed symmetric function symmetric group three letters tion transitive true if operated tutions xlt x2