A New Conjecture Concerning Admissibility of Groups

A finite group is said to be admissible if it has a permutation mapping of the form g → θ(g) such that g → g.θ(g) is also a permutation. Two different necessary conditions for a group to be admissible are known. For abelian groups both are sufficient and for soluble groups at least one. Here, we show that both conditions are satisfied by all finite non-soluble groups and so we conjecture that all such groups may be admissible