THE STRONG π-SYLOW THEOREM FOR THE GROUPS PSL2(q)

Let pi be a set of primes. A finite group G is a pi-group if all prime divisors of the order of G belong to pi. Following Wielandt, the pi-Sylow theorem holds for G if all maximal pi-subgroups of G are conjugate; if the pi-Sylow theorem holds for every subgroup of G then the strong pi-Sylow theorem holds for G. The strong pi-Sylow theorem is known to hold for G if and only if it holds for every nonabelian composition factor of G. In 1979, Wielandt asked which finite simple nonabelian groups obey the strong pi-Sylow theorem. By now the answer is known for sporadic and alternating groups. We give some arithmetic criterion for the validity of the strong pi-Sylow theorem for the groups PSL2(q).