On two theorems of Thompson
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- by Guang Xiang Zhang PDF
- Proc. Amer. Math. Soc. 98 (1986), 579-582 Request permission
Abstract:
Let $G$ be a finite group. Theorem. Let $P \in {\operatorname {Syl} _p}(G)$ with ${\Omega _1}(P) \leq Z(P)$. If ${N_G}(Z(P))$ has a normal $p$-complement, then so does $G$. Corollary. Let $M$ be a nilpotent maximal subgroup of $G$ and $P \in {\operatorname {Syl} _2}(M)$ with ${\Omega _2}(P) \leq Z(P)$. Then $G$ is solvable. This extends Thompson’s solvability theorem [9]. We also give two other results generalizing Thompson’s theorem.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 579-582
- MSC: Primary 20D20
- DOI: https://doi.org/10.1090/S0002-9939-1986-0861754-6
- MathSciNet review: 861754