Warren Nichols, Bettina Richmond
Let H be a cosemisimple Hopf algebra over an algebraically closed field k. We show that if H contains a simple subcoalgebra of dimension 4, then H contains either a Hopf subalgebra of dimension 2, 12, or 60, or a simple subcoalgebra of dimension n^2 for each positive integer n. In particular, if H is finite dimensional, then it has even dimension.