Оn the soluble radical of the finite groups

  • S. Yu. Bashun Polotz. state University, Belarus
  • E. M. Palchik Polotz. state University, Belarus

Abstract

UDC 512.542<br>

We assume that $G$ is a finite group, $\pi(G)=\{s\}\cup \sigma$, $s > 2$, $\Sigma$ is a set of Sylow$\sigma$-subgroups taken one for each $p_i\in \sigma$, $R(G)$ is the largest normal soluble subgroup in $G$ (the soluble radical of $G$). Suppose also that each Sylow $p_i$-subgroup $G_{p_i}\in \Sigma$ normalizes thes-subgroup $T^{(i)}\neq 1$ of the group $G$. With these assumptions, we determine the conditions under whichs divides $|R(G)|$.

 

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Published
28.03.2020
How to Cite
BashunS. Y., and Palchik E. M. “Оn the Soluble Radical of the Finite Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 3, Mar. 2020, pp. 326-39, doi:10.37863/umzh.v72i3.800.
Section
Research articles