Geodesic
Criteria of $p$-supersolubility and supersolubility of finite groups
Problemy fiziki, matematiki i tehniki, no. 1 (2011), pp. 57-61.

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Let $G$ be a finite group, $A$ a subgroup of $G$. Then we say that $A$ is generalized quasinormal in $G$ if $A$ either covers or avoids every maximal pair $(K,H)$ of $G$. We say that $A$ is $m$-supplemented in $G$ if $G$ has a subgroup $T$ and a generalized quasinormal subgroup $C$ such that $G = AT$ and $T \cap A \le C \le A$. Based on these concepts new characterizations of finite $p$-supersoluble and supersoluble groups are obtained.
Mots-clés : maximal pair
Keywords: generalized quasinormal subgroup, $m$-supplemented subgroup, $p$-supersoluble group, supersoluble group. 
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V. A. Kovaleva; A. N. Skiba. Criteria of $p$-supersolubility and supersolubility of finite groups. Problemy fiziki, matematiki i tehniki, no. 1 (2011), pp. 57-61. http://geodesic.mathdoc.fr/item/PFMT_2011_1_a8/

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