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On the Coincidence of the Classes of Finite Groups $ E_{\pi_{x}} $ and $ D_{\pi_{x}} $
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2021-01-29 , DOI: 10.1134/s0037446621010055
K. A. Ilenko , N. V. Maslova

Let \( \pi_{x} \) be the set of primes greater than \( x \). We prove that for all \( x\in{𝕉} \) the classes of finite groups \( D_{\pi_{x}} \) and \( E_{\pi_{x}} \) coincide; i.e., a finite group \( G \) possesses a \( \pi_{x} \)-Hall subgroup if and only if \( G \) satisfies the complete analog of the Sylow Theorems for a \( \pi_{x} \)-subgroup.



中文翻译:

关于有限组类的重合$ E _ {\ pi_ {x}} $和$ D _ {\ pi_ {x}} $

\(\ pi_ {x} \)为大于\(x \)的素数集 。我们证明对于所有 \(x \ in {𝕉} \)有限群的类别\(D _ {\ pi_ {x}} \)\(E _ {\ pi_ {x}} \)是 一致的;也就是说,一个有限群\(G \)拥有一个\(\ pi_ {x} \)-霍尔子群,并且仅当 \(G \)满足\(\ pi_ {x}的Sylow定理的完全类比时 \)-子组。

更新日期:2021-02-02
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