Note On (m, 2, m -1, (m-2)/2) Relative Difference Sets

摘要

In this note, we consider relative difference sets with the parameter (m, 2, m -1, (m-2)/2) in a group G relative to a subgroup N. In the splitting case, G = H x N, we give a lower bound for the size of the commutator group H', and we show that H can not have a homomorphic image which is generalized dihedral. In the non-splitting case, we prove that there is no (2n, 2, 2n-1, n-1) relative difference set in a generalized dihedral group of order 4n, n > 1.