Nonnilpotent subsets in the Suzuki groups
| Autor: | Mohammad Zarrin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | International Journal of Group Theory, Vol 6, Iss 2, Pp 7-15 (2017) |
| Druh dokumentu: | article |
| ISSN: | 2251-7650 2251-7669 |
| DOI: | 10.22108/ijgt.2017.11176 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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