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The Progress on \(6\)-Transposition Groups

Michael Turner

University of Birmingham

Time: 16:00-17:00 (GMT+8), Wednesday March 12th, 2025
Location: Zoom


Abstract: A finite 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 \(k\). Around 1970, Fischer investigated \(3\)-transposition groups and discovered three new sporadic simple groups. Looking at larger transposition groups, he predicted the Baby Monster and Monster simple groups. We will start the talk with 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 ongoing progress on classifying the simple, almost simple, and quasisimple \(6\)-transposition groups. This is joint work with Chris Parker.


Host: 尹富纲 Fu-Gang Yin