Nonnilpotent subsets in the Suzuki groups

International Journal of Group Theory

Mohammad Zarrin¹ 

[1] University of Kurdistan;

关键词: Nilpotentlizer;    Hypercenter of a group;    Clique number;    Graphs associated to groups;   

DOI  :  10.22108/ijgt.2017.11176

来源: DOAJ

【 摘 要 】

Let $G$ be a group and $mathcal{N}$ be the class of all nilpotent groups. A subset $A$ of $G$ is said to be nonnilpotent if for any two distinct elements $a$ and $b$ in $A$, $langle a, brangle notin mathcal{N}$. If, for any other nonnilpotent subset $B$ in $G$, $|A|geq |B|$, then $A$ is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by $omega(mathcal{N}_G)$. In this paper, among other results, we obtain $omega(mathcal{N}_{Suz(q)})$ and $omega(mathcal{N}_{PGL(2,q)})$, where $Suz(q)$ is the Suzuki simple group over the field with $q$ elements and $PGL(2,q)$ is the projective general linear group of degree $2$ over the finite field with $q$ elements, respectively.

【 授权许可】

Unknown