Upper and Lower Semimodularity of the Supercharacter Theory Lattices of Cyclic Groups

2012/03/07 by Benidt, Samuel G., Hall, William R. S., Hendrickson, Anders O. F.
#20C15 (Primary) 06C10 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1203.1638

Abstract

We consider the lattice of supercharacter theories, in the sense of Diaconis and Isaacs, of the cyclic group of order n. We find necessary and sufficient conditions on n for that lattice to be upper or lower semimodular.

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