TY - JOUR
T1 - On Finite Groups Whose Nilpotentisers Are Nilpotent Subgroups
AU - Amiri , Seyyed Majid Jafarian
AU - Rostami , Hojjat
JO - Journal of Mathematical Study
VL - 4
SP - 307
EP - 313
PY - 2018
DA - 2018/04
SN - 50
DO - http://doi.org/10.4208/jms.v50n4.17.01
UR - https://global-sci.org/intro/article_detail/jms/11319.html
KW - Finite group, nilpotentiser, $\mathcal{N}$-group.
AB - <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>