On divisible difference sets which are fixed by the inverse (Q1825873)

Let G be a finite group of order mn with a subgroup N of order n. A k- element subset D of G is called an \((m,n,k,\lambda_ 1,\lambda_ 2)\)- divisible difference set if the expressions \(d_ 1d_ 2^{-1}\), for \(d_ 1\) and \(d_ 2\) in D with \(d_ 1\neq d_ 2\), represent each element in \(G\setminus N\) exactly \(\lambda_ 2\) times and each element in \(N\setminus \{e\}\) exactly \(\lambda_ 1\) times. In this paper, we study the particular case that D is fixed by the inverse, that is, \(D^{(-1)}=\{g^{-1}| g\in D\}=D\). Existence and nonexistence results will be given.