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1992 | 141 | 3 | 215-227
Tytuł artykułu

On soluble groups of automorphisms of nonorientable Klein surfaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
141
Numer
3
Strony
215-227
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-11-26
poprawiono
1992-02-11
Twórcy
autor
  • Institute of Mathematics, Pedagogical University (WSP), Chodkiewicza 30, 85-064 Bydgoszcz, Poland
Bibliografia
  • [1] N. L. Alling and N. Greenleaf, Foundations of the Theory of Klein Surfaces, Lecture Notes in Math. 219, Springer, 1971.
  • [2] E. Bujalance, Proper periods of normal NEC subgroups with even index, Rev. Math. Hisp.-Amer. 41 (4) (1981), 121-127.
  • [3] E. Bujalance, Normal subgroups of NEC groups, Math. Z. 178 (1981), 331-341.
  • [4] E. Bujalance, J. J. Etayo, J. M. Gamboa and G. Gromadzki, Automorphism Groups of Compact Bordered Klein Surfaces, Lecture Notes in Math. 1439, Springer, 1990.
  • [5] E. Bujalance and G. Gromadzki, On nilpotent groups of automorphisms of compact Klein surfaces, Proc. Amer. Math. Soc. 108 (3) (1990), 749-759.
  • [6] B. P. Chetiya, Groups of automorphisms of compact Riemann surfaces, Ph.D. thesis, Birmingham University, 1981.
  • [7] B. P. Chetiya, On genuses of compact Riemann surfaces admitting solvable automorphism groups, Indian J. Pure Appl. Math. 12 (1981), 1312-1318.
  • [8] B. P. Chetiya and K. Patra, On metabelian groups of automorphisms of compact Riemann surfaces, J. London Math. Soc. 33 (1986), 467-472.
  • [9] H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 3rd ed., Ergeb. Math. Grenzgeb. 14, Springer, Berlin 1972.
  • [10] N. Greenleaf and C. L. May, Bordered Klein surfaces with maximal symmetry, Trans. Amer. Math. Soc. 274 (1982), 265-283.
  • [11] G. Gromadzki, On soluble groups of automorphisms of Riemann surfaces, Canad. Math. Bull. 34 (1) (1991), 67-73.
  • [12] A. Hurwitz, Ueber algebraische Gebilde mit eindeutigen Transformationen in sich, Math. Ann. 41 (1893), 403-442.
  • [13] A. M. Macbeath, The classification of non-euclidean plane crystallographic groups, Canad. J. Math. 19 (1967), 1192-1205.
  • [14] C. L. May, Automorphisms of compact Klein surfaces with boundary, Pacific J. Math. 59 (1975). 199-210.
  • [15] C. L. May, Large automorphism groups of compact Klein surfaces with boundary I, Glasgow Math. J. 18 (1977), 1-10.
  • [16] C. L. May, The species of Klein surfaces with maximal symmetry of low genus, Pacific J. Math. 111 (2) (1984), 371-394.
  • [17] C. L. May, Supersolvable M*-groups, Glasgow Math. J. 30 (1988), 31-40.
  • [18] K. Oikawa, Note on conformal mappings of a Riemann surface onto itself, Kodai Math. Sem. Rep. 8 (1956), 23-30.
  • [19] R. Preston, Projective structures and fundamental domains on compact Klein surfaces, Ph.D. thesis, Univ. of Texas, 1975.
  • [20] D. Singerman, Automorphisms of compact non-orientable Riemann surfaces, Glasgow Math. J. 12 (1971), 50-59.
  • [21] D. Singerman, On the structure of non-Euclidean crystallographic groups, Proc. Cambridge Philos. Soc. 76 (1974), 233-240.
  • [22] D. Singerman, Orientable and non-orientable Klein surfaces with maximal symmetry, Glasgow Math. J. 26 (1985), 31-34.
  • [23] M. C. Wilkie, On non-euclidean crystallographic groups, Math. Z. 91 (1966), 87-102.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv141i3p215bwm
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