University of Isfahan International Journal of Group Theory 2251-7650 3 4 2014 12 01 A note on the Normalizer of sylow 2-subgroup of special linear group SL2(pf) 33 36 4976 10.22108/ijgt.2014.4976 EN Jiangtao Shi Yantai University Journal Article 2013 11 22 Let $G={\rm SL}_2(p^f)$ be a special linear group and $P$ be a Sylow‎ ‎$2$-subgroup of $G$‎, ‎where $p$ is a prime and $f$ is a positive‎ ‎integer such that $p^f>3$‎. ‎By $N_G(P)$ we denote the normalizer of‎ ‎$P$ in $G$‎. ‎In this paper‎, ‎we show that $N_G(P)$ is nilpotent (or‎ ‎$2$-nilpotent‎, ‎or supersolvable) if and only if $p^{2f}\equiv‎ ‎1\,({\rm mod}\,16)$‎. https://ijgt.ui.ac.ir/article_4976_a69c9b523546d6cc0812f1d9027240e7.pdf