On the order of transitive permutation groups with cyclic point-stabilizer

Andrea Lucchini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1998)

  • Volume: 9, Issue: 4, page 241-243
  • ISSN: 1120-6330

Abstract

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If G is a transitive permutation group of degree n with cyclic point-stabilizer, then the order of G is at most n 2 ⁢ − ⁢ n .

How to cite

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Lucchini, Andrea. "On the order of transitive permutation groups with cyclic point-stabilizer." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.4 (1998): 241-243. <http://eudml.org/doc/252382>.

@article{Lucchini1998,
abstract = {If \( G \) is a transitive permutation group of degree \( n \) with cyclic point-stabilizer, then the order of \( G \) is at most \(n^\{2\} − n \).},
author = {Lucchini, Andrea},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Permutation groups; Transitivity; Normal-core; transitive permutation groups; cyclic point-stabilizers; order bounds},
language = {eng},
month = {12},
number = {4},
pages = {241-243},
publisher = {Accademia Nazionale dei Lincei},
title = {On the order of transitive permutation groups with cyclic point-stabilizer},
url = {http://eudml.org/doc/252382},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Lucchini, Andrea
TI - On the order of transitive permutation groups with cyclic point-stabilizer
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/12//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 4
SP - 241
EP - 243
AB - If \( G \) is a transitive permutation group of degree \( n \) with cyclic point-stabilizer, then the order of \( G \) is at most \(n^{2} − n \).
LA - eng
KW - Permutation groups; Transitivity; Normal-core; transitive permutation groups; cyclic point-stabilizers; order bounds
UR - http://eudml.org/doc/252382
ER -

References

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  1. Babai, L. - Goodman, A. J. - Pyber, L., Groups without faithful transitive permutation representations of small degree. J. Algebra, vol. 195, 1997, 1-29. Zbl0886.20020MR1468882DOI10.1006/jabr.1997.7042
  2. Chermak, A. - Delgado, A., A measuring argument for finite group. Proc. Amer. Math. Soc., vol. 107, 1989, 907-914. Zbl0687.20022MR994774DOI10.2307/2047648
  3. Pyber, L., Asymptotic results for simple groups and some applications. In: L. Finkelstein (ed.), Groups and Computation II DIMACS Series in Discrete Mathematics and Theoretical Computer Science. Amer. Math. Soc., Providence, vol. 28, 1997, 309-327. Zbl0887.20006MR1444143

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