Title: Frobenius groups and retract rationality

Speaker: 康明昌教授（台湾大学）

Venue: 数学研究中心82号甲乙丙楼82J13教室

Time: 4:30-5:30 pm, April 19, 2012 (Thursday)

Abstract: Frobenius groups arise naturally in various questions of group cohomology, differential geometry, algebraic topology, etc. We will show that k(G) is retract k-rational if G is a Frobenius group and k is an infinite field satisfying very mild conditions. As an application, we will show that, if k is any algebraic number field, G is a Frobenius group whose complement is isomorphic to SL(2; 5), then the inverse Galois problem is true, i.e. there is a Galois field extension K over k such that Gal(K/k) is isomorphic to SL(2; 5). More generally, for an algebraic number field K such that k(z_8)/k is a cyclic extension and for any non-solvable Frobenius group G, the inverse Galois problem is true for k and G.