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Fundam. Prikl. Mat., 2005, Volume 11, Issue 3, Pages 119–125 (Mi fpm835)  

On a problem from the Kourovka Notebook

S. V. Larin

Krasnoyarsk State Pedagogical University named after V. P. Astaf'ev

Abstract: In this article, it is proved that if a group $G$ coincides with its commutator subgroup, is generated by a finite set of classes of conjugate elements, and contains a proper minimal normal subgroup $A$ such that the factor group $G/A$ coincides with the normal closure of one element, then $G$ coincides with the normal closure of an element. From this a positive answer to question 5.52 from the Kourovka Notebook for the group with the condition of minimality on normal subgroups follows. We have found a necessary and sufficient condition for a group coinciding with its commutator subgroup and generated by a finite set of classes of conjugate elements not to coincide with the normal closure of any element.

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English version:
Journal of Mathematical Sciences (New York), 2007, 144:2, 3955–3959

Bibliographic databases:

UDC: 512.544

Citation: S. V. Larin, “On a problem from the Kourovka Notebook”, Fundam. Prikl. Mat., 11:3 (2005), 119–125; J. Math. Sci., 144:2 (2007), 3955–3959

Citation in format AMSBIB
\Bibitem{Lar05}
\by S.~V.~Larin
\paper On a~problem from the Kourovka Notebook
\jour Fundam. Prikl. Mat.
\yr 2005
\vol 11
\issue 3
\pages 119--125
\mathnet{http://mi.mathnet.ru/fpm835}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2176683}
\zmath{https://zbmath.org/?q=an:1110.20024}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 144
\issue 2
\pages 3955--3959
\crossref{https://doi.org/10.1007/s10958-007-0248-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34250222425}


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  • Фундаментальная и прикладная математика
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