Communications in Mathematics |
The greatest power of a prime $p$ dividing the natural number $n$ will be denoted by $n_p$. Let $Ind_G(g)=|G:C_G(g)|$. Suppose that $G$ is a finite group and $p$ is a prime. We prove that if there exists an integer $\alpha>0$ such that $Ind_G(a)_p\in \{1,p^{\alpha}\}$ for every $a$ of $G$ and a $p$-element $x\in G$ such that $Ind_G(x)_p>1$, then $G$ includes a normal $p$-complement.
Source : ScholeXplorer
IsRelatedTo ARXIV math/0506294 Source : ScholeXplorer IsRelatedTo DOI 10.1007/s10469-005-0037-5 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0506294
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