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PFMT, 2019, Issue 2(39), Pages 76–80 (Mi pfmt641)  

MATHEMATICS

Finite factored groups with soluble $\mathbb{X}$-subnormal factors

V. N. Kniahinaa, I. K. Chirikb

a F. Scorina Gomel State University
b University of Civil Protection of the Ministry for Emergency Situations of the Republic of Belarus, Minsk

Abstract: 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, soluble group, factored group, generalized subnormal subgroup.

Full text: PDF file (346 kB)
References: PDF file   HTML file
UDC: 512.542
Received: 20.01.2019

Citation: V. N. Kniahina, I. K. Chirik, “Finite factored groups with soluble $\mathbb{X}$-subnormal factors”, PFMT, 2019, no. 2(39), 76–80

Citation in format AMSBIB
\Bibitem{KnyChi19}
\by V.~N.~Kniahina, I.~K.~Chirik
\paper Finite factored groups with soluble $\mathbb{X}$-subnormal factors
\jour PFMT
\yr 2019
\issue 2(39)
\pages 76--80
\mathnet{http://mi.mathnet.ru/pfmt641}


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