FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 3, PAGES 119-125

**On a problem from the Kourovka Notebook**

S.
V.
Larin

Abstract

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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.

Location: http://mech.math.msu.su/~fpm/eng/k05/k053/k05308h.htm

Last modified: September 14, 2005