ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 20 Kiechle, Hubert, TU München, Germany Frobenius groups with many involutions A Frobenius group is a (possibly infinite) group which acts transitively, but not regularly on a set such that one point stabilizers are fixed point free. Frobenius groups with a transitive subset of involutions are characterized as quasidirect products of a K-loop L by an appropriate automorphism group of L. This generalizes the famous theorem for certain finite Frobenius groups. It also generalizes Karzel’s approach to describe sharply 2-transitive groups using neardomains.