Southeast Asian Bulletin of Mathematics, Volume (44), No (6), Year (2020-11) , Pages (797-802)

Title : ( Some Notes on Non-inner Nilpotent Groups )

Authors: masoumeh ganjali , Ahmad Erfanian , I. Muchtadi-Alamsyah ,

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The purpose of this paper is to state some new results on an -nilpotent group, which was introduced by Barzegar and the second author, for any fixed auto- morphism of a group G. They investigated some properties of an -nilpotent group and proved that an -nilpotent group is nilpotent but the converse is not valid in gen- eral. Therefore, authors tried to prepare some conditions that under what conditions a nilpotent group is -nilpotent for an automorphism . A group G is said to be non-inner nilpotent, whenever it is nilpotent related to a non-inner automorphism of the group G. In this paper, we provide some examples of non-inner nilpotent groups, also we prove that every nilpotent group of maximal class is non-inner nilpotent and we try to classify all finite non-abelian non-inner nilpotent groups of order pn, n 5, for an odd prime p. Central automorphisms fixing the center of a group element-wise may play an important role to this classification.


, Central automorphism; Inner automorphism; Nilpotent group; Non, inner nilpotent group.
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author = {Ganjali, Masoumeh and Erfanian, Ahmad and I. Muchtadi-Alamsyah},
title = {Some Notes on Non-inner Nilpotent Groups},
journal = {Southeast Asian Bulletin of Mathematics},
year = {2020},
volume = {44},
number = {6},
month = {November},
issn = {0129-2021},
pages = {797--802},
numpages = {5},
keywords = {Central automorphism; Inner automorphism; Nilpotent group; Non-inner nilpotent group.},


%0 Journal Article
%T Some Notes on Non-inner Nilpotent Groups
%A Ganjali, Masoumeh
%A Erfanian, Ahmad
%A I. Muchtadi-Alamsyah
%J Southeast Asian Bulletin of Mathematics
%@ 0129-2021
%D 2020