Advanced search
Publication Cover
Communications in Algebra Volume 32, 2004 - Issue 1
Submit an article Journal homepage
87
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Influence of Indices of the Maximal Subgroups of the Finite Simple Groups on the Structure of a Finite Group

Xianhua Li Department of Mathematics, Suzhou University, Suzhou, Jiangsu, P.R. China; Department of Mathematics, Suzhou University, 1 Shizi St., Suzhou, 215006, Jiangsu, P.R. ChinaCorrespondence[email protected]
Pages 33-64 | Published online: 10 Oct 2011

References

  • Arad , Z. and Fisman , E. 1984 . On finite factorizable groups . J. Algebra , 86 : 522 – 548 .
  • Aschbacher , M. 1984 . On the maximal subgroups of the finite classical groups . Invent. Math. , 76 : 465 – 514 .
  • Carter , R. W. 1972 . Simple Groups of Lie Type New York : Wiley-Interscience .
  • Carter , R. and Fong , P. 1964 . The Sylow 2-subgroups of the finite classical groups . J. Algebra , 1 : 139 – 151 .
  • Chen , Z. 1988 . Inner-Outer-∑ Groups and Minimal Non-∑ Groups (in Chinese) Chongqing Beibei : Southwest China Normal University Publishing House .
  • Cohen , A. M. , Liebeck , M. W. , Saxl , J. and Seitz , G. M. 1992 . The local maximal subgroups of exceptional groups of Lie type, finite and algebraic . Proc. London Math. Soc. , 64 ( 3 ) : 21 – 48 .
  • Conway , J. H. , Curtis , R. T. , Norton , S. P. , Parker , R. A. and Wilson , R. A. 1985 . Atlas of Finite Groups Oxford : Clarendon Press .
  • Cooperstein , B. N. 1978 . Minimal degree for a permutaion representation of a classical group . Israel J. Mathematics , 30 ( 3 ) : 213 – 235 .
  • Curtis , C. W. , Kantor , W. M. and Seitz , G. M. 1976 . The 2-transitive permutation representations of the finite Chevally groups . Trans Am. Math. Socc. , 218 : 1 – 59 .
  • Dixon , J. D. and Mortimer , B. 1996 . Permutation Groups Berlin : Spring-Verlag .
  • Fray , R. D. 1967 . Congruence properties of ordinary and q-binomial coefficients . Duke Math. J. , 34 : 467 – 480 .
  • Gorenstein , D. 1982 . Finite Simple Groups New York and London : Plenum Press .
  • Gorenstein , D. and Lyons , R. 1983 . The local structure of finite grops of characteristic 2 type . Mem. Am. Math. Soc. , 276 : 1 – 731 .
  • Gross , F. 1986 . On a conjecture of Philip Hall . Proc. London Math. Soc. , 52 : 464 – 494 .
  • Guralnick , R. M. 1982 . Subgroups of prime power index in a simple group . J. Algebra , 81 : 304 – 311 .
  • Hua , L. 1957 . Introduction to Number Theory Beijing : Chinese Science Press .
  • Huppert , B. 1979 . Endiche Gruppen I, II Berlin : Spring-Verlag .
  • Kimmerle , W. , Lyons , R. , Sandling , R. and Teague , D. N. 1990 . Composition factors from the group ring and Artin's theorem on orders of simple groups . Proc. London Math. Soc. , 60 ( 3 ) : 89 – 122 .
  • King , O. 1982 . Imprimitive maximal subgroups of the general linear, special linear, simplectic and general symplectic groups . J. London Math. Soc. , 25 ( 2 ) : 416 – 424 .
  • King , O. 1983 . Imprimitive maximal subgroups of the orthogonal, special orthogonal, unitary and special unitary groups . Math. Z. , 182 : 193 – 203 .
  • Kleidman , P. B. 1987 . The maximal subgroups of the finite 8-dimensional orthogonal groups P (q) and of their automorphism groups . J. Algebra , 110 : 173 – 242 .
  • Kleidman , P. B. 1988 . The maximal subgroups of the Steinberg triality 3 D 4(q) and of their automorphism groups . J. Algebra , 115 : 182 – 199 .
  • Kleidman , P. B. 1988 . The maximal subgroups of the Chevalley groups G 2(q) with q odd, the Ree groups 2 G 2(q), and their automorphism groups . J. Algebra , 117 : 30 – 71 .
  • Kleidman , P. and Liebeck , M. 1990 . The Subgroup Structure of the Finite Classical Groups Cambridge : Cambridge University Press .
  • Kleidman , P. B. and Wilson , R. A. 1988 . The maximal subgroups of J 4 . Proc. London Math. Soc. , 56 ( 3 ) : 484 – 510 .
  • Kleidman , P. B. , Parker , R. A. and Wilson , R. A. 1989 . The maximal subgroups of the Fischer Group Fi 23 . J. London Math. Soc. , 39 ( 2 ) : 89 – 101 .
  • Li , X. 1995 . A quantitative characterization of finite simple group . Chinese Science Bull. , 40 ( 16 ) : 1329 – 1332 .
  • Li , X. 2001 . A characterization of finite simple group . J. Algebra , 245 : 620 – 649 .
  • Li , X. and Wang , D. 2002 . A quantitative property of sporadic simple groups . J. Group Theory , 5 : 41 – 52 .
  • Liebeck , M. W. 1985 . On the order of maximal subgroups of the finite classical groups . Proc. London Math. Soc. , 50 ( 3 ) : 426 – 446 .
  • Liebeck , M. W. and Saxl , J. 1985a . The primitive permutation groups of containing an element of larger prime order . J. London Math. Soc. , 31 ( 2 ) : 237 – 249 .
  • Liebeck , M. W. and Saxl , J. 1985b . The primitive permutation groups of odd degree . J. London Math. Soc. , 31 ( 2 ) : 250 – 260 .
  • Liebeck , M. W. , Prager , C. E. and Saxl , J. 1987a . On the order of maximal subgroups of the finite exceptional groups of Lie type . Proc. London Math. Soc. , 55 ( 3 ) : 299 – 330 .
  • Liebeck , M. W. , Prager , C. E. and Saxl , J. 1987b . A classifcation of the maximal subgroups of the finite Alternating and Symmetric groups . J. Algebra , 111 : 365 – 383 .
  • Liebeck , M. W. , Prager , C. E. and Saxl , J. 1990 . The maximal factorization of the finitesimple groups and their automorphism groups . Mem. Am. Math. Soc. , 86 ( 432 ) : 1 – 151 .
  • Liebeck , M. W. , Saxl , J. and Seitz , G. M. 1992 . Subgroups of maximal rank in groups of Lie type . Proc. London Math. Soc. , 65 ( 3 ) : 297 – 325 .
  • Linton , S. 1989 . The maximal subgroups of the Thompson group . J. London Math. Soc. , 39 ( 2 ) : 79 – 88 .
  • Linton , S. A. and Wilson , R. A. 1991 . The maximal subgroups of the Fischer groups Fi 24 and . Proc. London Math. Soc. , 65 : 113 – 164 .
  • Malle , G. 1991 . The maximal subgroups of 2 F 4(q 2) . J. Algebra , 139 : 52 – 69 .
  • Robinson , D. J. S. 1982 . A Course in the Theory of Groups New York, Heidelberg, Berlin : Springer Verlag .
  • Rose , J. S. 1978 . A Course on Group Theory Cambridge University Press .
  • Thompson , J. G. 1966 . Hall subgroups of the symmetric groups . J. Combinatorial Theory , 1 : 271 – 279 .
  • Weir , A. J. 1955 . Sylow p-subgroups of the classical groups over finite fields with characteristic prime to p . Proc. Am. Math. Soc. , 6 : 529 – 533 .
  • Wielandt , H. 1964 . Finite Permutation Groups New York/London : Academic Press .
  • Williams , J. S. 1981 . Prime graph components of finite groups . J. Algebra , 69 : 487 – 513 .
  • Wilson , R. A. 1984 . On maximal subgroups of Fi 22 . Math. Proc. Cambridge Philos. Soc. , 95 : 197 – 222 .
  • Wilson , R. A. 1987 . The local subgroups of the Fischer groups . J. London Math. Soc. , 36 ( 2 ) : 77 – 94 .
  • Wilson , R. A. 1999 . The maximal subgroups of the Baby Monster, I . J. Algebra , 211 : 1 – 14 .
  • Zhang , Y. 1984 . The Structure of the Finite Groups Beijing : Chinese Science Press .
  • #Communicated by A. Yu Olshanskii.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.