Algebraic function fields with solvable automorphism group in characteristic p

Finite Groups as Galois Groups of Function Fields With Infinite Field of Constants

“…The constant field of M 1 is k 1 and M = M 1 N . This implies that g M = g M 1 , and by (3) it follows that g M 1 > C. 2 PROPOSITION 4.2. Suppose that K /k is a function field such that K /k(y) is a finite extension, where K 0 is the separable closure of k(y) in K .…”

“…Madden and Valentini [6] proved that every finite group can be realized as the full automorphism group of an algebraic function field K /k. D'Mello and Madan [3] established the theorem of Greenberg in the case where G is a solvable group G and K = k(x) is a rational function field.…”

“…D'Mello and Madan [3] established the theorem of Greenberg in the case where G is a solvable group G and K = k(x) is a rational function field.…”

“…As a consequence of this variant of the Castelnuovo-Severi inequality, we have the analogue of a result of Madden and Valentini [6] that establishes that if L/K is an extension such that every proper intermediate field has large enough genus, then for any automorphism σ of L, we have σ (K ) = K . [3] Finite groups as Galois groups of function fields with infinite field of constants 303…”