## Tohoku Mathematical Journal 2003 June SECOND SERIES VOL. 55, NO. 2

 Tohoku Math. J. 55 (2003), 271-282

Title RIGID BRAID ORBITS RELATED TO $\mathrm{PSL}_2(p^2)$ AND SOME SIMPLE GROUPS

Author Takehito Shiina

(Received May 23, 2001)
Abstract. We apply the braid orbit theorem to projective semilinear groups over the finite fields with $p^2$ elements and some almost simple groups of Lie type. The projective special linear groups $\mathrm{PSL}_2(p^2)$ with $p\equiv\pm 3 (\mod 8)$, the Tits simple group, and some small simple groups occur regularly as Galois groups over the rationals.

2000 Mathematics Subject Classification. Primary 12F12; Secondary 20D06, 20F36.

Key words and phrases. Inverse Galois problem, finite simple groups, braid actions.