Displaying similar documents to “On supersoluble groups acting on Klein surfaces.”

A family of M-surfaces whose automorphism groups act transitively on the mirrors.

Adnan Melekoglu (2000)

Revista Matemática Complutense

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Let X be a compact Riemmann surface of genus g > 1. A symmetry T of X is an anticonformal involution. The fixed point set of T is a disjoint union of simple closed curves, each of which is called a mirror of T. If T fixes g +1 mirrors then it is called an M-symmetry and X is called an M-surface. If X admits an automorphism of order g + 1 which cyclically permutes the mirrors of T then we shall call X an M-surface with the M-property. In this paper we investigate those M-surfaces...

On ovals on Riemann surfaces.

Grzegorz Gromadzki (2000)

Revista Matemática Iberoamericana

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We prove that k (k ≥ 9) non-conjugate symmetries of a Riemann surface of genus g have at most 2g - 2 + 2(9 - k) ovals in total, where r is the smallest positive integer for which k ≤ 2. Furthermore we prove that for arbitrary k ≥ 9 this bound is sharp for infinitely many values of g.

Big groups of automorphisms of some Klein surfaces.

Beata Mockiewicz (2002)

RACSAM

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Sea X una superficie de Klein compacta con borde de gen algebraico p ≥ 2. Se sabe que si G es un grupo de automorfismos de X entonces |G| ≤ 12(p- 1). Se dice que G es un grupo grande de gen p si |G| > 4(p -1). En el presente artículo se halla una familia de enteros p para los que el único grupo grande de gen p son los grupos diédricos. Esto significa que, en términos del gen real introducido por C. L. May, para tales valores de p no existen grupos grandes de gen real p. ...

Lifting di-analytic involutions of compact Klein surfaces to extended-Schottky uniformizations

Rubén A. Hidalgo (2011)

Fundamenta Mathematicae

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Let S be a compact Klein surface together with a di-analytic involution κ: S → S. The lowest uniformizations of S are those whose deck group is an extended-Schottky group, that is, an extended Kleinian group whose orientation preserving half is a Schottky group. If S is a bordered compact Klein surface, then it is well known that κ can be lifted with respect to a suitable extended-Schottky uniformization of S. In this paper, we complete the above lifting property by proving that if S...

On pq-hyperelliptic Riemann surfaces

Ewa Tyszkowska (2005)

Colloquium Mathematicae

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A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ϱ, called a p-hyperelliptic involution, for which X/ϱ is an orbifold of genus p. If in addition X admits a q-hypereliptic involution then we say that X is pq-hyperelliptic. We give a necessary and sufficient condition on p,q and g for existence of a pq-hyperelliptic Riemann surface of genus g. Moreover we give some conditions under which p- and q-hyperelliptic involutions of...