OD-characterization of almost simple groups related to L 2 ( 49 )

Liang Cai Zhang; Wu Jie Shi

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 3, page 191-199
  • ISSN: 0044-8753

Abstract

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In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group L 2 ( 49 ) . As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to L 2 ( 49 ) except L 2 ( 49 ) · 2 2 . Also, we prove that if M is an almost simple group related to L 2 ( 49 ) except L 2 ( 49 ) · 2 2 and G is a finite group such that | G | = | M | and Γ ( G ) = Γ ( M ) , then G ≅ M .

How to cite

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Zhang, Liang Cai, and Shi, Wu Jie. "OD-characterization of almost simple groups related to $L_{2}(49)$." Archivum Mathematicum 044.3 (2008): 191-199. <http://eudml.org/doc/250481>.

@article{Zhang2008,
abstract = {In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group $L_\{2\}(49)$. As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to $L_\{2\}(49)$ except $L_\{2\}(49)\cdot 2^\{2\}$. Also, we prove that if $M$ is an almost simple group related to $L_\{2\}(49)$ except $L_\{2\}(49)\cdot 2^\{2\}$ and $G$ is a finite group such that $|G|=|M|$ and $\Gamma (G)=\Gamma (M)$, then $G\cong M$.},
author = {Zhang, Liang Cai, Shi, Wu Jie},
journal = {Archivum Mathematicum},
keywords = {almost simple group; prime graph; degree of a vertex; degree pattern; almost simple groups; prime graphs; degrees of vertices; degree patterns; order components; sets of element orders; projective special linear groups},
language = {eng},
number = {3},
pages = {191-199},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {OD-characterization of almost simple groups related to $L_\{2\}(49)$},
url = {http://eudml.org/doc/250481},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Zhang, Liang Cai
AU - Shi, Wu Jie
TI - OD-characterization of almost simple groups related to $L_{2}(49)$
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 3
SP - 191
EP - 199
AB - In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group $L_{2}(49)$. As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to $L_{2}(49)$ except $L_{2}(49)\cdot 2^{2}$. Also, we prove that if $M$ is an almost simple group related to $L_{2}(49)$ except $L_{2}(49)\cdot 2^{2}$ and $G$ is a finite group such that $|G|=|M|$ and $\Gamma (G)=\Gamma (M)$, then $G\cong M$.
LA - eng
KW - almost simple group; prime graph; degree of a vertex; degree pattern; almost simple groups; prime graphs; degrees of vertices; degree patterns; order components; sets of element orders; projective special linear groups
UR - http://eudml.org/doc/250481
ER -

References

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