Ilya Gorshkov - On existence of normal p-complement of finite groups with restrictions on the conjugacy class sizes

cm:9294 - Communications in Mathematics, May 12, 2022, Volume 30 (2022), Issue 1 - https://doi.org/10.46298/cm.9294
On existence of normal p-complement of finite groups with restrictions on the conjugacy class sizes

Authors: Ilya Gorshkov

    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.


    Volume: Volume 30 (2022), Issue 1
    Published on: May 12, 2022
    Accepted on: April 5, 2022
    Submitted on: April 3, 2022
    Keywords: Mathematics - Group Theory

    Linked publications - datasets - softwares

    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
    • math/0506294
    • 10.48550/arxiv.math/0506294
    • 10.1007/s10469-005-0037-5
    • 10.1007/s10469-005-0037-5
    An adjacency criterion for the prime graph of a finite simple group

    Consultation statistics

    This page has been seen 181 times.
    This article's PDF has been downloaded 76 times.