Аннотация:
Let
$G$
be a group, and let
$\operatorname{Hom}(G,N)$
be the group of all
homomorphisms of
$G$
into an Abelian subgroup
$N$
of
$G$.
We give here a necessary
condition for finitely generated groups
to satisfy the condition that
$\operatorname{Hom}(G/L,N)$
is isomorphic to
$G/M$,
where
$L\le M$,
$L$
and
$M$
are normal subgroups of
$G$.
Consequently, we also extend
some existing results on equality of two automorphism groups.
Ключевые слова:homomorphism group, nilpotent group, absolute central automorphisms.
