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• W2516792835 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 every $seq{A,g}$ for all $gin G$. 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 $cin C$ for which $A$ is subnormal in $seq{A,c}$. 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.
• W2516792835 created "2016-09-16" @default.
• W2516792835 creator A5071690473 @default.
• W2516792835 creator A5075638024 @default.
• W2516792835 date "2016-08-16" @default.
• W2516792835 modified "2023-09-27" @default.
• W2516792835 title "A generalisation of a theorem of Wielandt" @default.
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