## Automorphism groups on compact Riemann surfaces |

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### Contents

Construction of Big Groups | 16 |

Sharpness of the Bounds | 27 |

Orbit Spaces of Higher Genus | 34 |

1 other sections not shown

### Common terms and phrases

antihomomorphism apply 2.l Assume G AUTOMORPHISM GROUPS big group bound is attained bound is sharp branch points Brown University ceenH Chapter commutator has order COMPACT RIEMANN SURFACES consider construction cover group covering is branched covering surface cyclic group Define r(a defining relations dihedral group erdor errdo fixed positive integers following theorem fundamental group genus g given genus group G group of automorphisms group of order homeomorphism implies imprimitivity of Eq induced representation infinitely many g's isomorphic kernel large groups Lemma Let G member of G monodromy theorem multiplicity n-sheeted normal covering normal subgroup notation o o o orbit space order of G path permutes the points points above pQ pougr pourg prime proof of 3.l Riemann Sphere semidirect product sequence of g's sets of imprimitivity subgroup of G surface of genus upper bound veah William Thomas Kiley