| Title:
|
On the prime graphs of the automorphism groups of sporadic simple groups (English) |
| Author:
|
Khosravi, Behrooz |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
83-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper as the main result, we determine finite groups with the same prime graph as the automorphism group of a sporadic simple group, except $J_2$. (English) |
| Keyword:
|
automorphism group of a sporadic simple group |
| Keyword:
|
prime graph |
| MSC:
|
05C25 |
| MSC:
|
20D05 |
| MSC:
|
20D08 |
| MSC:
|
20D45 |
| MSC:
|
20D60 |
| idZBL:
|
Zbl 1204.20028 |
| idMR:
|
MR2591665 |
| . |
| Date available:
|
2009-06-25T18:17:01Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128298 |
| . |
| Reference:
|
[1] Chen, Z. M., Shi, W. J.: On simple $C_{pp}$ groups.J. Southwest China Teachers Univ. 18 (3) (1993), 249–256. |
| Reference:
|
[2] Chigira, N., Iiyori, N., Yamaki, H.: Non-abelian Sylow subgroups of finite groups of even order.Invent. Math. 139 (2000), 525–539. Zbl 0961.20017, MR 1738059, 10.1007/s002229900040 |
| Reference:
|
[3] Conway, J., Curtis, R., Norton, S., Parker, R., Wilson, R.: Atlas of finite groups.Clarendon Press, Oxford, 1985. Zbl 0568.20001 |
| Reference:
|
[4] Crescenzo, P.: A diophantine equation which arises in the theory of finite groups.Adv. Math. 17 (1975), 25–29. Zbl 0305.10016, MR 0371812, 10.1016/0001-8708(75)90083-3 |
| Reference:
|
[5] Gorenstein, D.: Finite groups.Harper and Row, New York, 1968. Zbl 0185.05701, MR 0231903 |
| Reference:
|
[6] Gruenberg, K. W., Roggenkamp, K. W.: Decomposition of the augmentation ideal and of the relation modules of a finite group.Proc. London Math. Soc. (3) 31 (2) (1975), 149–166. Zbl 0313.20004, MR 0374247 |
| Reference:
|
[7] Hagie, M.: The prime graph of a sporadic simple group.Comm. Algebra 31 (9) (2003), 4405–4424. Zbl 1031.20009, MR 1995543, 10.1081/AGB-120022800 |
| Reference:
|
[8] Iranmanesh, A., Alavi, S. H., Khosravi, B.: A characterization of $PSL(3,q)$ where $q$ is an odd prime power.J. Pure Appl. Algebra 170 (2-3) (2002), 243–254. Zbl 1001.20005, MR 1904845, 10.1016/S0022-4049(01)00113-X |
| Reference:
|
[9] Janson, C., Lux, K., Parker, R. A., Wilson, R. A.: An atlas of Brauer characters.Clarendon Press, Oxford, 1995. MR 1367961 |
| Reference:
|
[10] Khosravi, A., Khosravi, B.: A new characterization of almost sporadic groups.J. Algebra Appl. 1 (3) (2002), 267–279. Zbl 1033.20013, MR 1932151, 10.1142/S021949880200015X |
| Reference:
|
[11] Khosravi, B.: $n$-recognition by prime graph ofthe simple group $PSL(2,q)$.J Algebra Appl. 7 (6) (2008), 735–748. MR 2483329, 10.1142/S0219498808003090 |
| Reference:
|
[12] Mazurov, V. D.: Characterization of finite groups by sets of orders of their elements.Algebra and Logic 36 (1) (1997), 23–32. MR 1454690, 10.1007/BF02671951 |
| Reference:
|
[13] Mazurov, V. D.: Recognition of finite groups by a set of orders of their elements.Algebra and Logic 37 (6) (1998), 371–379. Zbl 0917.20021, MR 1680412, 10.1007/BF02671691 |
| Reference:
|
[14] Praeger, C. E., Shi, W. J.: A characterization of some alternating and symmetric grops.22 (5) (1994), 1507–1530. MR 1264726 |
| Reference:
|
[15] Shi, W., Bi, J.: A characteristic property for each finite projective special linear group.Lecture Notes in Math. 1456 (1990), 171–180. Zbl 0718.20009, MR 1092230, 10.1007/BFb0100738 |
| Reference:
|
[16] Zsigmondy, K.: Zur Theorie der Potenzreste.Monatsh. Math. Phys. 3 (1892), 265–284. MR 1546236 |
| . |
