Simple groups without involutions
Seminar Room 1, Newton Institute
Bad groups are simple groups of finite Morley rank whose proper, definable, connected subgroups are nilpotent. Their existence is a well-known open problem in the analysis of simple groups of finite Morley rank and would refute the Cherlin-Zilber algebraicity conjecture.
One of the striking properties of bad groups is that they do not have involutions. Another one is that their proper, maximal, definable, connected subgroups intersect trivially. These properties are shared by other classes of simple groups of finite Morley rank that are not bad in the above sense. In a sense there is more than one notion of badness. In the talk I will mention some of these bad classes and make some remarks about the reduction of some open problems to a bad configuration.