On soluble groups of automorphisms of nonorientable Klein surfaces

G. Gromadzki

Fundamenta Mathematicae (1992)

  • Volume: 141, Issue: 3, page 215-227
  • ISSN: 0016-2736

Abstract

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We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.

How to cite

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Gromadzki, G.. "On soluble groups of automorphisms of nonorientable Klein surfaces." Fundamenta Mathematicae 141.3 (1992): 215-227. <http://eudml.org/doc/211961>.

@article{Gromadzki1992,
abstract = {We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.},
author = {Gromadzki, G.},
journal = {Fundamenta Mathematicae},
keywords = {Riemann surfaces; Klein surfaces; automorphism groups; soluble groups; symmetries of surfaces; automorphisms; compact Riemann surfaces; compact non-orientable Klein surfaces; soluble group of automorphisms; maximal symmetry groups; bordered Klein surfaces; maximal symmetry},
language = {eng},
number = {3},
pages = {215-227},
title = {On soluble groups of automorphisms of nonorientable Klein surfaces},
url = {http://eudml.org/doc/211961},
volume = {141},
year = {1992},
}

TY - JOUR
AU - Gromadzki, G.
TI - On soluble groups of automorphisms of nonorientable Klein surfaces
JO - Fundamenta Mathematicae
PY - 1992
VL - 141
IS - 3
SP - 215
EP - 227
AB - We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.
LA - eng
KW - Riemann surfaces; Klein surfaces; automorphism groups; soluble groups; symmetries of surfaces; automorphisms; compact Riemann surfaces; compact non-orientable Klein surfaces; soluble group of automorphisms; maximal symmetry groups; bordered Klein surfaces; maximal symmetry
UR - http://eudml.org/doc/211961
ER -

References

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