Upper and Lower Semimodularity of the Supercharacter Theory Lattices of Cyclic Groups
Samuel G. Benidt, William R. S. Hall, Anders O. F. Hendrickson · Communications in Algebra · 2013
We consider the lattice of supercharacter theories, in the sense of Diaconis and Isaacs [5 Diaconis , P. , Isaacs , I. M. ( 2008 ). Supercharacters and superclasses for algebra groups . Trans. Amer. Math. Soc. 360 : 2359 – 2392 .[Crossref], [Web of Science ®] , [Google Scholar]], of the cyclic group of order n. We find necessary and sufficient conditions on n for that lattice to be upper or lower semimodular.