Geodesic
On $\sigma$-properties of finite groups~I
Problemy fiziki, matematiki i tehniki, no. 4 (2014), pp. 89-96

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Let $\sigma=\{\sigma_i|i \in I\}$ be some partition of the set $\mathbb{P}$ of all primes, that is, $\mathbb{P}=\bigcup_{i\in I}\sigma_i$ and $\sigma_i\cap\sigma_j=\varnothing$ for all $i\ne j$. We say that a finite group $G$ is: $\sigma$-primary if $G$ is a $\sigma_i$-group for some $\sigma_i\in\sigma$; a $\sigma$-group if $G$ has a set $\mathcal{H}=\{H_1, \dots, H_t\}$ of Hall subgroups such that $H_i$ is $\sigma$-primary, $(|H_i|, |H_j|)=1$ for all $i\ne j$ and $\pi(G)=\pi(H_1)\cup\dots\cup\pi(H_t)$. We analyze some properties of finite $\sigma$-groups.
Keywords: finite group, Hall subgroup, $\pi$-separable group.
Mots-clés : $\sigma$-group, $\sigma$-soluble group 
@article{PFMT_2014_4_a12,
     author = {A. N. Skiba},
     title = {On $\sigma$-properties of finite {groups~I}},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {89--96},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_4_a12/}
}
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A. N. Skiba. On $\sigma$-properties of finite groups~I. Problemy fiziki, matematiki i tehniki, no. 4 (2014), pp. 89-96. http://geodesic.mathdoc.fr/item/PFMT_2014_4_a12/