The University of Arizona

The 3-modular character table of the automorphism group of the O'Nan group

The 3-modular character table of the automorphism group of the O'Nan group

Series: Algebra and Number Theory Seminar
Location: ENR2 S395
Presenter: Klaus Lux, U of A

One of the open problems of the modular Atlas project (www.math.rwth-aachen.de/~MOC/work.html) is the determination of the 3-modular character table of ON.2,  the automorphism group of the O'Nan group ON. Recently, a connection of the O'Nan group to the theory of elliptic curves has  been described in "Pariah Moonshine" by Duncan, Mertens, and Ono, see https://www.nature.com/articles/s41467-017-00660-y.  In this talk we give a survey  of the properties of ON and ON.2, and describe how we determined  the 3-modular character table using theoretical and computational methods.  The main tools involved are character theoretic and condensation.  This is joint work with A. Ryba, Queens College, N.Y.

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