A characterization property of the simple group PSL 4 ( 5 ) 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

Abstract

top
Let ω ( G ) denote the set of element orders of a finite group G . If H is a finite non-abelian simple group and ω ( H ) = ω ( 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 P S L 4 ( 5 ) is quasirecognizable.

How to cite

top

Darafsheh, 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 -

References

top
  1. Aleeva M. R., On finite simple groups with the set of element orders as in a Frobenius group or a double Frobenius group, Math. Notes 73 3-4 (2003), 299–313. Zbl1065.20025MR1992593
  2. Brandl R., Shi W. J., The characterization of P S L ( 2 , q ) by its element orders, J. Algebra, 163 (1) (1994), 109–114. (1994) MR1257307
  3. Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A., Atlas of Finite Groups, Clarendon Press, Oxford, 1985. (1985) Zbl0568.20001MR0827219
  4. Darafsheh M. R., Karamzadeh N. S., A characterization of groups P S L ( 3 , q ) by their element orders for certain q , J. Appl. Math. Comput. (old KJCAM) 9 (2) (2002), 409–421. MR1895684
  5. Darafsheh M. R., Some conjugacy classes in groups associated with the general linear groups, Algebras Groups Geom. 15 (1998), 183–199. (1998) Zbl0995.20027MR1676998
  6. Darafsheh M. R., Farjami Y., Calculating the set of orders of elements in the finite linear groups, submitted. Zbl1154.20040
  7. Gorenstein D., Finite groups, Harper and Row, New York, 1968. (1968) Zbl0185.05701MR0231903
  8. Higman G., Finite groups in which every element has prime power order, J. London Math. Soc. 32 (1957), 335–342. (1957) Zbl0079.03204MR0089205
  9. Kleidman P., Liebeck M., The subgroup structure of finite classical groups, Cambridge University Press, 1990. (1990) MR1057341
  10. Kondratjev A. S., On prime graph components of simple groups, Math. Sb. 180 (6) (1989), 787–797. (1989) 
  11. Lipschutz S., Shi W. J., Finite groups whose element orders do not exceed twenty, Progr. Natur. Sci. 10 (1) (2000), 11–21. MR1765567
  12. Mazurov V. D., Xu M. C., Cao H. P., Recognition of finite simple groups L 3 ( 2 m ) and U 3 ( 2 m ) by their element orders, Algebra Logika 39 (5) (2000), 567–585. MR1805756
  13. Mazurov V. D., Characterization of finite groups by sets of orders of their elements, Algebra Logika 36 (1) (1997), 37–53. (1997) MR1454690
  14. Passman D. S., Permutation groups, W. A. Bengamin, New York, 1968. (1968) Zbl0179.04405MR0237627
  15. Shi W. J., A characteristic property of 𝔸 5 , J. Southwest-China Teachers Univ. (B) 3 (1986), 11–14. (1986) MR0915854
  16. Shi W. J., A characteristic property of P S L 2 ( 7 ) , J. Austral. Math. Soc. (A) 36 (3) (1984), 354–356. (1984) MR0733907
  17. Shi W. J., A characterization of some projective special linear groups, J. Southwest-China Teachers Univ. (B) 2 (1985), 2–10. (1985) Zbl0597.20007MR0843760
  18. Shi W. J., A characteristic property of J 1 and P S L 2 ( 2 n ) , Adv. Math. (in Chinese) 16 (4) (1987), 397–401. (1987) 
  19. Shi W., Bi J., A characteristic property for each finite projective special linear group, Lecture Notes in Math. 1456 (1990), 171–180. (1990) Zbl0718.20009MR1092230
  20. Willams J. S., Prime graph components of finite groups, J. Algebra 69 (2) (1981), 487–513. (1981) MR0617092

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.