The depth of the maximal subgroups of Ree groups

被引：5
作者：
Hethelyi, Laszlo [1 ]
Horvath, Erzsebet [1 ]
Petenyi, Franciska [1 ]
机构：
[1] Budapest Univ Technol & Econ, Dept Algebra, Muegyet Rkp 3-9, H-1521 Budapest, Hungary
来源：
COMMUNICATIONS IN ALGEBRA | 2019年 / 47卷 / 01期
关键词：
Ree groups; combinatorial depth; ordinary depth; maximal subgroup; primitive action; base size; subdegree; PSL(2;
D O I：
10.1080/00927872.2018.1461885
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We determine the combinatorial and the ordinary depth of the maximal subgroups of the simple Ree groups (2)G(2)(q). As an application of these calculations, we determine the subdegrees of primitive actions of the groups (2)G(2)(q). We also improve an earlier estimate of Burness, Liebeck, and Shalev on the base size of" non-standard" primitive actions of (2)G(2)(q) on the coset space of maximal subgroups from 3 to 2.
引用
收藏
页码：37 / 66
页数：30
相关论文
共 50 条
  • [21] Bounds on the Number of Maximal Subgroups of Finite Groups
    Ballester-Bolinches, Adolfo
    Esteban-Romero, Ramon
    Jimenez-Seral, Paz
    RESULTS IN MATHEMATICS, 2023, 78 (01)
  • [22] On Prime Spectrum of Maximal Subgroups in Finite Groups
    Zhang, Chi
    Guo, Wenbin
    Maslova, Natalia V.
    Revin, Danila O.
    ALGEBRA COLLOQUIUM, 2018, 25 (04) : 579 - 584
  • [23] Finite simple groups with complemented maximal subgroups
    V. M. Levchuk
    A. G. Likharev
    Siberian Mathematical Journal, 2006, 47 : 659 - 668
  • [24] On a class of groups with given cofactors of maximal subgroups
    L. P. Avdashkova
    S. F. Kamornikov
    Mathematical Notes, 2010, 87 : 601 - 607
  • [25] On a class of groups with given cofactors of maximal subgroups
    Avdashkova, L. P.
    Kamornikov, S. F.
    MATHEMATICAL NOTES, 2010, 87 (5-6) : 601 - 607
  • [26] Finite groups with decomposable cofactors of maximal subgroups
    Lemeshev, I. V.
    Monakhov, V. S.
    TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2011, 17 (04): : 181 - 188
  • [27] FINITE GROUPS WITH SOLVABLE OR Φ-SIMPLE MAXIMAL SUBGROUPS
    Bazhanova, E. N.
    SIBERIAN MATHEMATICAL JOURNAL, 2022, 63 (04) : 611 - 619
  • [28] Finite simple groups with complemented maximal subgroups
    Levchuk, V. M.
    Likharev, A. G.
    SIBERIAN MATHEMATICAL JOURNAL, 2006, 47 (04) : 659 - 668
  • [29] X-permutable maximal subgroups of Sylow subgroups of finite groups
    Guo W.
    Shum K.P.
    Skiba A.N.
    Ukrainian Mathematical Journal, 2006, 58 (10) : 1471 - 1480
  • [30] FINITE GROUPS WHOSE MAXIMAL SUBGROUPS HAVE ONLY SOLUBLE PROPER SUBGROUPS
    Lytkina, D. V.
    Zhurtov, A. Kh.
    SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2022, 19 (01): : 237 - 240
12345