Towards a classification of 6-transposition groups
Algebra Seminar
4th February 2025, 4:00 pm – 5:00 pm
Fry Building, 2.04
A group along with a normal set of involutions, D, is called a k-transposition group if D generates the group and the product of any two distinct elements in D has order at most k. In 1970, Fischer investigated 3-transposition groups and found three new sporadic simple groups. He also predicted the Baby Monster and Monster simple groups by looking at larger transposition groups. We will start with some examples before discussing the history of transposition groups. Next, we will look at basic observations and results. The rest of the talk will be focused on the progress so far on simple, almost simple, and quasisimple groups with this 6-transposition group property. Understanding what happens with these groups will give us an insight for a classification of finite 6-transposition groups. This is joint work with Chris Parker.
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