Title:
|
Some results on the recognizability of the linear groups over the binary field (English) |
Author:
|
Darafsheh, M. R. |
Author:
|
Farjami, Y. |
Author:
|
Khademi, M. |
Author:
|
Moghaddamfar, A. R. |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
46 |
Issue:
|
4 |
Year:
|
2005 |
Pages:
|
589-600 |
. |
Category:
|
math |
. |
Summary:
|
In this paper, we first find the set of orders of all elements in some special linear groups over the binary field. Then, we will prove the characterizability of the special linear group $\operatorname{PSL}(13,2)$ using only the set of its element orders. (English) |
Keyword:
|
element order |
Keyword:
|
prime graph |
Keyword:
|
projective special linear group |
MSC:
|
05C25 |
MSC:
|
20D05 |
MSC:
|
20D06 |
MSC:
|
20D60 |
idZBL:
|
Zbl 1106.20009 |
idMR:
|
MR2259492 |
. |
Date available:
|
2009-05-05T16:53:40Z |
Last updated:
|
2012-04-30 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119552 |
. |
Reference:
|
[1] Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A.: Atlas of Finite Groups.Clarendon Press, Oxford, 1985. Zbl 0568.20001, MR 0827219 |
Reference:
|
[2] Darafsheh M.R.: Some conjugacy classes in groups associated with the general linear groups.Algebras Groups Geom. 15 (1998), 183-199. Zbl 0995.20027, MR 1676998 |
Reference:
|
[3] Darafsheh M.R., Moghaddamfar A.R.: Characterization of the groups $PSL_5(2)$, $PSL_6(2)$ and $PSL_7(2)$.Comm. Algebra 29 1 (2001), 465-475. MR 1842510 |
Reference:
|
[4] Darafsheh M.R., Moghaddamfar A.R.: Corrigendum to: ``Characterization of the groups $PSL_5(2)$, $PSL_6(2)$ and $PSL_7(2)$''.Comm. Algebra 32 9 (2003), 4651-4653. MR 1995557 |
Reference:
|
[5] Darafsheh M.R., Moghaddamfar A.R.: A characterization of groups related to the linear groups $PSL(n,2)$, $n=5,6,7,8$.Pure Math. Appl. 11 4 (2000), 629-637. MR 1876305 |
Reference:
|
[6] Dornhoff L.: Group Representation Theory. Part A: Ordinary Representation Theory.Marcel Dekker, New York, 1971. MR 0347959 |
Reference:
|
[7] Green J.A.: The characters of the finite general linear groups.Trans. Amer. Math. Soc. 80 (1955), 402-447. Zbl 0068.25605, MR 0072878 |
Reference:
|
[8] Kondratév A.S.: On prime graph components of finite simple groups.Mat. Sb. (1989), 180 6 787-797. MR 1015040 |
Reference:
|
[9] Kleidman P., Liebeck M.: The subgroup structure of the finite classical groups.London Math. Soc. Lecture Note Series 129, 1990. Zbl 0697.20004, MR 1057341 |
Reference:
|
[10] Lidl R., Niederreiter H.: Finite Fields.Addison-Wesley, 1983. Zbl 1139.11053, MR 0746963 |
Reference:
|
[11] Lucido M.S., Moghaddamfar A.R.: Groups with complete prime graph connected components.J. Group Theory 7 3 (2004), 373-384. Zbl 1058.20014, MR 2063403 |
Reference:
|
[12] Mazurov V.D.: Characterization of groups by arithmetic properties.Algebra Colloq. 11 1 (2004), 129-140. MR 2058968 |
Reference:
|
[13] Shi W.J.: A characteristic property of $A_{8}$.Acta Math. Sinica (N.S.) 3 (1987), 92-96. MR 0915854 |
Reference:
|
[14] Shi W.J.: The characterization of the sporadic simple groups by their elements orders.Algebra Colloq. 1 2 (1994), 156-166. MR 1272290 |
Reference:
|
[15] Shi W.J.: A characteristic property of $A_{5}$ (Chinese).J. Southwest-China Teachers University 11 (3) (1986), 11-14. MR 0915854 |
Reference:
|
[16] Shi W.J., Wang L.H., Wang S.H.: The pure quantitative characterization of linear groups over the binary field (Chinese).Chinese Ann. Math. Ser. A 24 6 (2003), 675-682. MR 2032168 |
Reference:
|
[17] Shi W.J.: A characterization property of $PSL_2(7)$.J. Austral. Math. Soc. 36 (1984), 354-356. |
Reference:
|
[18] Williams J.S.: Prime graph components of finite groups.J. Algebra 69 (1981), 487-513. Zbl 0471.20013, MR 0617092 |
. |