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 $p^{2f}\equiv 1\,({\rm mod}\,16)$.
B. Huppert (1967). Endliche Gruppen I. Springer-Verlag, Berlin. D. J. S. Robinson (1996). A Course in the Theory of Groups. (Second Edition),
Springer-Verlag, New York.
Shi, J. (2014). A note on the Normalizer of sylow 2-subgroup of special linear group SL2(pf). International Journal of Group Theory, 3(4), 33-36. doi: 10.22108/ijgt.2014.4976
MLA
Jiangtao Shi. "A note on the Normalizer of sylow 2-subgroup of special linear group SL2(pf)", International Journal of Group Theory, 3, 4, 2014, 33-36. doi: 10.22108/ijgt.2014.4976
HARVARD
Shi, J. (2014). 'A note on the Normalizer of sylow 2-subgroup of special linear group SL2(pf)', International Journal of Group Theory, 3(4), pp. 33-36. doi: 10.22108/ijgt.2014.4976
VANCOUVER
Shi, J. A note on the Normalizer of sylow 2-subgroup of special linear group SL2(pf). International Journal of Group Theory, 2014; 3(4): 33-36. doi: 10.22108/ijgt.2014.4976
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