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• W2000762423 abstract "Several problems in the theory of finite permutation groups considered before by H. Wielandt are attacked by new and traditional methods. One new method is given by the theorem that a semisimple subgroup A of a group G normalizing a different subgroup B isomorphic to A forces that the centralizer in AB of B is non-trivial, hence B is not the generalized Fitting subgroup of its normalizer. This theorem is applied in proving that the paired subconstituent G α Δ ′ ( α ) of a primitive permutation group G is faithful if the non-trivial subconstituent G α Δ ( α ) is regular. If G α Δ ( α ) is a non-abelian simple group all of whose proper subgroups are solvable then the regularity of G α Δ ( α ) even implies that G α Δ ( α ) is faithful. Also several theorems are obtained for the case that a non-trivial subconstituent G α Δ ( α ) is nilpotent or, more generally, that G α β is subnormal in G α for β ∈ Δ ( α ) ." @default.
• W2000762423 created "2016-06-24" @default.
• W2000762423 creator A5086370833 @default.
• W2000762423 date "2006-08-01" @default.
• W2000762423 modified "2023-09-29" @default.
• W2000762423 title "Some problems of Wielandt revisited" @default.
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• W2000762423 doi "https://doi.org/10.1016/j.jalgebra.2005.09.013" @default.
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