RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (102 kB)
References: PDF file   HTML file

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}