2014/05/07 by Lang, Alexander
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1405.1764
We describe the supercharacter theories of the semidirect product of H and K, H\rtimes K in terms of the supercharacter theories of the direct product of H and K in the case when both H and K are Abelian groups. To do this we introduce the concept of a homomorphism of supercharacter theories. This provides a classification of the supercharacter theories of the dihedral groups of order 2m when m is odd using the known classification of the supercharacter theories of cyclic groups.