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A new characterization of Mathieu groups

Changguo Shao; Qinhui Jiang

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 1, page 13-23
  • ISSN: 0044-8753

Abstract

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Let G be a finite group and nse ( G ) the set of numbers of elements with the same order in G . In this paper, we prove that a finite group G is isomorphic to M , where M is one of the Mathieu groups, if and only if the following hold: (1)  | G | = | M | , (2)  nse ( G ) = nse ( M ) .

How to cite

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Shao, Changguo, and Jiang, Qinhui. "A new characterization of Mathieu groups." Archivum Mathematicum 046.1 (2010): 13-23. <http://eudml.org/doc/37650>.

@article{Shao2010,
abstract = {Let $G$ be a finite group and $\operatorname\{nse\}(G)$ the set of numbers of elements with the same order in $G$. In this paper, we prove that a finite group $G$ is isomorphic to $M$, where $M$ is one of the Mathieu groups, if and only if the following hold: (1) $|G|=|M|$, (2) $\operatorname\{nse\}(G)=\operatorname\{nse\}(M)$.},
author = {Shao, Changguo, Jiang, Qinhui},
journal = {Archivum Mathematicum},
keywords = {finite group; solvable group; order of element; finite simple groups; Mathieu groups; numbers of elements; sets of element orders; orders of finite groups},
language = {eng},
number = {1},
pages = {13-23},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A new characterization of Mathieu groups},
url = {http://eudml.org/doc/37650},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Shao, Changguo
AU - Jiang, Qinhui
TI - A new characterization of Mathieu groups
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 1
SP - 13
EP - 23
AB - Let $G$ be a finite group and $\operatorname{nse}(G)$ the set of numbers of elements with the same order in $G$. In this paper, we prove that a finite group $G$ is isomorphic to $M$, where $M$ is one of the Mathieu groups, if and only if the following hold: (1) $|G|=|M|$, (2) $\operatorname{nse}(G)=\operatorname{nse}(M)$.
LA - eng
KW - finite group; solvable group; order of element; finite simple groups; Mathieu groups; numbers of elements; sets of element orders; orders of finite groups
UR - http://eudml.org/doc/37650
ER -

References

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