Note on the special linear homogeneous group

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a note on the normalizer of sylow 2-subgroup of special linear group $sl_2(p^f)$

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 $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

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ژورنال

عنوان ژورنال: Bulletin of the American Mathematical Society

سال: 1896

ISSN: 0002-9904

DOI: 10.1090/s0002-9904-1896-00359-1