# A characterization property of the simple group ${\mathrm{PSL}}_{4}\left(5\right)$ by the set of its element orders

Mohammad Reza Darafsheh; Yaghoub Farjami; Abdollah Sadrudini

Archivum Mathematicum (2007)

- Volume: 043, Issue: 1, page 31-37
- ISSN: 0044-8753

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topDarafsheh, Mohammad Reza, Farjami, Yaghoub, and Sadrudini, Abdollah. "A characterization property of the simple group ${\rm PSL}_4(5)$ by the set of its element orders." Archivum Mathematicum 043.1 (2007): 31-37. <http://eudml.org/doc/250173>.

@article{Darafsheh2007,

abstract = {Let $\omega (G)$ denote the set of element orders of a finite group $G$. If $H$ is a finite non-abelian simple group and $\omega (H)=\omega (G)$ implies $G$ contains a unique non-abelian composition factor isomorphic to $H$, then $G$ is called quasirecognizable by the set of its element orders. In this paper we will prove that the group $PSL_\{4\}(5)$ is quasirecognizable.},

author = {Darafsheh, Mohammad Reza, Farjami, Yaghoub, Sadrudini, Abdollah},

journal = {Archivum Mathematicum},

keywords = {projective special linear group; element order; projective special linear groups; sets of element orders; quasirecognizable groups},

language = {eng},

number = {1},

pages = {31-37},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {A characterization property of the simple group $\{\rm PSL\}_4(5)$ by the set of its element orders},

url = {http://eudml.org/doc/250173},

volume = {043},

year = {2007},

}

TY - JOUR

AU - Darafsheh, Mohammad Reza

AU - Farjami, Yaghoub

AU - Sadrudini, Abdollah

TI - A characterization property of the simple group ${\rm PSL}_4(5)$ by the set of its element orders

JO - Archivum Mathematicum

PY - 2007

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 043

IS - 1

SP - 31

EP - 37

AB - Let $\omega (G)$ denote the set of element orders of a finite group $G$. If $H$ is a finite non-abelian simple group and $\omega (H)=\omega (G)$ implies $G$ contains a unique non-abelian composition factor isomorphic to $H$, then $G$ is called quasirecognizable by the set of its element orders. In this paper we will prove that the group $PSL_{4}(5)$ is quasirecognizable.

LA - eng

KW - projective special linear group; element order; projective special linear groups; sets of element orders; quasirecognizable groups

UR - http://eudml.org/doc/250173

ER -

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