Intersections of primary subgroups in nonsoluble finite groups isomorphic to \(L_n(2^m)\). (English. Russian original) Zbl 1406.20027
Sib. Math. J. 59, No. 2, 264-269 (2018); translation from Sib. Mat. Zh. 59, No. 2, 337-344 (2018).
Summary: Given a finite group \(G\) with socle isomorphic to \(L_n(2^m)\), we describe (up to conjugacy) all ordered pairs of primary subgroups \(A\) and \(B\) in \(G\) such that \(A\cap B^g\neq 1\) for all \(g\in G\).
MSC:
| 20D20 | Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20D25 | Special subgroups (Frattini, Fitting, etc.) |
References:
| [1] | Burnside, W., On groups of order \(p\)\^{}{a}\(q\)\^{}{b} (second paper), Proc. London Math. Soc., 2, 432-437, (1985) · JFM 36.0198.02 |
| [2] | Monakhov, V. S., Invariant subgroups of biprimary subgroups, Math. Notes, 18, 1109-1114, (1975) · Zbl 0355.20021 · doi:10.1007/BF01099991 |
| [3] | Passman, D. S., Groups with normal solvable Hall p-subgroups, Trans. Amer. Math. Soc., 123, 99-111, (1966) · Zbl 0139.01801 |
| [4] | Zenkov, V. I., The intersections of nilpotent subgroups in finite groups, Fund. Prikl. Mat., 2, 1-92, (1996) · Zbl 0905.20011 |
| [5] | Zenkov, V. I.; Mazurov, V. D., The intersection of Sylow subgroups in finite groups, Algebra and Logic, 35, 236-240, (1996) · Zbl 0880.20011 · doi:10.1007/BF02367025 |
| [6] | Zenkov, V. I., On intersections of nilpotent subgroups in finite symmetric and alternating groups, Proc. Steklov Inst. Math., 285, 203-208, (2014) · Zbl 1304.20007 · doi:10.1134/S0081543814050228 |
| [7] | Zenkov, V. I., On intersections of primary subgroups in the group aut(\(L\)_{n}(2)), Proc. Steklov Inst. Math., 293, 270-277, (2016) · Zbl 1352.20018 · doi:10.1134/S0081543816050230 |
| [8] | Zenkov, V. I., Intersection of abelian subgroups in finite groups, Math. Notes, 56, 869-871, (1994) · Zbl 0839.20032 · doi:10.1007/BF02110750 |
| [9] | Jamali, A. R.; Viseh, M., On nilpotent subgroups containing nontrivial normal subgroups, J. Group Theory, 13, 411-416, (2010) · Zbl 1195.20018 |
| [10] | 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). · Zbl 0568.20001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
