# MMath thesis on Mathieu groups

My MMath student, Sam Hughes, recently submitted his dissertation entitled “*Representation and character theory of the small Mathieu groups*”; a copy is here.

The dissertation studies the ordinary (complex) character theory of *M _{11}* and

*M*; it includes the foundations of character theory, as well as details on how to construct

_{12}*M*and

_{11}*M*via the notion of “transitive extension”. I think Sam has done a beautiful job and should be congratulated!

_{12}We are in the process of writing up a paper including some of Sam’s results. In fact the paper comes from a slightly different point of view. Our main result is the following:

**Theorem**

- If
*G*is a sharply 5-transitive subgroup of Alt(12), then the character table of*G*is given by Table ***. - If
*G*is a sharply 4-transitive subgroup of Alt(11), then the character table of*G*is given by Table ***.

The point of this theorem is that we are able to construct the character table of *G* using only the assumption about multiple-transitivity – there is no direct reference to the Mathieu groups in this paper.

In the course of this research, I asked a question on MathOverflow here. Now seems a good time to thank the contributors to that discussion, especially Frieder Ladisch, for their help!