Abstract
Under study is the influence of the index of H in 〈H,H g〉 for g ∈ G on the structure of a group G, where H is either a second maximal subgroup of G or a Sylow subgroup of G.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Huppert B., Endliche Gruppen. I, Springer-Verlag, Berlin, Heidelberg, and New York (1967).
Doerk K. and Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin and New York (1992).
Robinson D. J. S., A Course in the Theory of Groups, Springer-Verlag, Berlin, Heidelberg, and New York (1982).
Chen Zh., Inner Outer Σ-Group and Minimal Non Σ-Group, Southwest Normal Univ. Press, Chongqing (1988).
Liebeck M. W., Prager C. E., and Saxl J., “A classification of the maximal subgroups of the finite alternating and symmetric groups,” J. Algebra, 111, 365–383 (1987).
Conway J. H., Curtis R. T., Norton S. P., Parker R. A., and Wilson R. A., Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups, Clarendon Press, Oxford (1985).
Liebeck M. W., Saxl J., and Seitz G. M., “Subgroups of maximal rank in groups of Lie type,” Proc. London Math. Soc., 65, No. 3, 297–325 (1992).
Kleidman P. and Liebeck M., The Subgroup Structure of the Finite Classical Groups, Cambridge Univ. Press, Cambridge (1990) (London Math. Soc. Lecture Notes; 129).
Thompson J. G., “Nonsolvable finite groups all of whose local subgroups are solvable. I,” Bull. Amer. Math. Soc., 74, No. 2, 383–437 (1968).
Guralnick R. M., “Subgroups of prime power index in a simple group,” J. Algebra, 81, No. 2, 304–311 (1983).
Suzuki M., “On a class of doubly transitive groups,” Ann. Math., 75, No. 2, 105–145 (1962).
Kurzweil H. and Stellmacher B., The Theory of Finite Groups: An Introduction, Springer-Verlag, New York, Berlin, and Heidelberg (2004).
Li C. and Seress A., “The primitive permutation groups of squarefree degree,” Bull. London Math. Soc., 35, No. 5, 635–644 (2003).
Flavell P., “Generating finite groups with conjugates of a subgroup. II,” J. Algebra, 232, 578–616 (2000).
Dixon J. D. and Mortimer B., Permutation Groups, Springer-Verlag, Berlin (1996).
Aschbacher M. and Guralnick R., “Solvable generation of groups and Sylow subgroups of the lower central series,” J. Algebra, 77, 189–201 (1982).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text Copyright © 2013 Li Xianhua and Zhang Xinjian
The authors were supported by the National Natural Science Foundation of China (Grants 11171243 and 10871032) and the Natural Science Foundation of the Jiangsu Province (Grant BK2008156).
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 826–837, July–August, 2013.
Rights and permissions
About this article
Cite this article
Li, X., Zhang, X. On indices of subgroups in the join of their conjugate pairs. Sib Math J 54, 656–665 (2013). https://doi.org/10.1134/S0037446613040071
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446613040071