A NOTE ON THE NORMALIZER OF SYLOW 2-SUBGROUP OF SPECIAL LINEAR GROUP SL_2(p^f)

Let G = SL2(pf ) 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 pf > 3. By NG(P) we denote the normalizer of P in G. In this paper, we show that NG(P) is nilpotent (or 2-nilpotent, or supersolvable) if and only if p2f  1 (mod 16).