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.) |
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