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Matematicheskie Zametki, 2020, Volume 108, Issue 1, paper published in the English version journal
(Mi mzm12410)
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Papers published in the English version of the journal
On Certain Automorphism Groups of Finitely Generated Groups
Sandeep Singh Deparment of Mathematics, Akal University, Talwandi Sabo, Punjab, 151003 India
Abstract:
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.
Keywords:
homomorphism group, nilpotent group, absolute central automorphisms.
Received: 12.04.2019 Revised: 29.04.2019
Citation:
Sandeep Singh, “On Certain Automorphism Groups of Finitely Generated Groups”, Math. Notes, 108:1 (2020), 142–145
Linking options:
https://www.mathnet.ru/eng/mzm12410
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