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- W2963840501 abstract "In 1974, Helmut Wielandt proved that in a finite group G , a subgroup A is subnormal if and only if it is subnormal in 〈 A , g 〉 for all g ∈ G . In this paper, we prove that the subnormality of an odd order nilpotent subgroup A of G is already guaranteed by a seemingly weaker condition: A is subnormal in G if for every conjugacy class C of G there exists c ∈ C for which A is subnormal in 〈 A , c 〉 . We also prove the following property of finite non-abelian simple groups: if A is a subgroup of odd prime order p in a finite almost simple group G , then there exists a cyclic p ′ -subgroup of F ⁎ ( G ) which does not normalise any non-trivial p -subgroup of G that is generated by conjugates of A ." @default.
- W2963840501 created "2019-07-30" @default.
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- W2963840501 date "2017-11-01" @default.
- W2963840501 modified "2023-09-27" @default.
- W2963840501 title "A generalisation of a theorem of Wielandt" @default.
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- W2963840501 doi "https://doi.org/10.1016/j.jalgebra.2017.07.006" @default.
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