On non-Abelian group difference sets
Let \(D\) be a symmetric \((v,k,\lambda)\)-design which admits an automorphism group \(\Gamma\) that acts sharply transitively on the points and lines of \(D\). Designs with this property can be described using difference sets. The normalizer \(N\) of \(\Gamma\) in the full automorphism group of a design is the group generated by \(\Gamma\) and the multiplier group of the difference set. The main theorem describes a construction of subgroups \(\Delta\) of \(N\) (different from \(\Gamma)\) which again act regularly on points and lines. The paper contains many examples and applications of the main theorem. An extended abstract of the paper has been published in [J. Sichuan Univ., Nat. Sci. Ed. 26, Spec. Issue, 136- 139 (1989; Zbl 0748.05027)].
scientific article; zbMATH DE number 179591