Geodesic
Finite factored groups with soluble $\mathbb{X}$-subnormal factors
Problemy fiziki, matematiki i tehniki, no. 2 (2019), pp. 76-80

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We establish new criteria of partial solubility of a finite factored group with restrictions on indices in chains of subgroups from factors to the group. In particular, it is proved that if $A$ and $B$ are soluble subgroups of a group $G$ such that there exist chains from $A$ and $B$ to $G$ in which indices of neighboring non-normal subgroups are either odd or equal to $2$ or $4$ and $G = AB$, then $G$ is soluble.
Keywords: finite group, factored group, generalized subnormal subgroup.
Mots-clés : soluble group 
@article{PFMT_2019_2_a10,
     author = {V. N. Kniahina and I. K. Chirik},
     title = {Finite factored groups with soluble $\mathbb{X}$-subnormal factors},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {76--80},
     publisher = {mathdoc},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2019_2_a10/}
}
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V. N. Kniahina; I. K. Chirik. Finite factored groups with soluble $\mathbb{X}$-subnormal factors. Problemy fiziki, matematiki i tehniki, no. 2 (2019), pp. 76-80. http://geodesic.mathdoc.fr/item/PFMT_2019_2_a10/