Author:
Taheri Hamid,Moghaddam Mohammd Reza R.,Rostamyari Mohammad Amin
Abstract
Abstract
Let G be a group and $$\mathrm{IA}(G)$$
IA
(
G
)
denote the group of all automorphisms of G, which induce identity map on the abelianized group $$G_{ab}=G/G'$$
G
ab
=
G
/
G
′
. Also the group of those $$\mathrm{IA}$$
IA
-automorphisms which fix the centre element-wise is denoted by $$\mathrm{IA_Z}(G)$$
IA
Z
(
G
)
. In the present article, among other results and under some condition we prove that the derived subgroups of finite p-groups, for which $$\mathrm{IA_Z}$$
IA
Z
-automorphisms are the same as central automorphisms, are either cyclic or elementary abelian.
Publisher
Springer Science and Business Media LLC
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1. On IA-Isoclinism of Groups;Journal of Algebra and Its Applications;2022-05-23