Оn the soluble radical of the finite groups
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...
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| Дата: | 2020 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2020
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/800 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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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| DOI: | 10.37863/umzh.v72i3.800 |