6-transposition Groups

Michael Turner, University of Birmingham

We call a group and a conjugacy class of involutions a k-transposition group if the class generates the group and any product of two elements in the class have order less than or equal to k. In 1970, Fischer investigated 3-transposition groups and as a result found three new sporadic simple groups. He also predicted the Baby Monster and Monster simple groups by looking at larger transposition groups. Since then, others have looked at certain transposition groups and produced classifications. In this talk, we will start by discussing the history before giving basic observations and results. The rest of the talk will be focused on the progress so far on simple, almost simple, and quasisimple groups and figuring out when they are or not 6-transposition groups. This is joint work with Chris Parker.