@Article{JMS-50-307,
author = {Amiri , Seyyed Majid Jafarian and Rostami , Hojjat},
title = {On Finite Groups Whose Nilpotentisers Are Nilpotent Subgroups},
journal = {Journal of Mathematical Study},
year = {2018},
volume = {50},
number = {4},
pages = {307--313},
abstract = {<p style="text-align: justify;">Let $G$ be a finite group and $x ∈ G.$ The nilpotentiser of $x$ in $G$ is defined to
be the subset $Nil_G(x) =\{y∈ G :\langle x,y \rangle \ is\ nilpotent\}.$ $G$ is called an $\mathcal{N}$-group ($n$-group) if $Nil_G(x)$ is a subgroup (nilpotent subgroup) of $G$ for all $x ∈ G\setminus Z^∗(G)$ where $Z^∗(G)$ is
the hypercenter of $G$. In the present paper, we determine finite $\mathcal{N}$-groups in which the
centraliser of each noncentral element is abelian. Also we classify all finite $n$-groups.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v50n4.17.01},
url = {http://global-sci.org/intro/article_detail/jms/11319.html}
}