Jordan-Hölder theorem for pseudo-symmetric sets (Q1086670)

A pseudo-symmetric set is a pair (\({\mathcal U},\sigma)\) where \({\mathcal U}\) is a set and \(\sigma\) is a mapping of \({\mathcal U}\) into the group of permutations on \({\mathcal U}\) such that \(u^{\sigma (u)}=u\) for every \(u\in {\mathcal U}\) and \(\sigma (u^{\sigma (v)})=\sigma (v)^{-1}\sigma (u)\sigma (v)\) for u,v\(\in {\mathcal U}\). In this paper the author establishes an analogue of the Jordan-Hölder theorem in group theory for pseudo-symmetric sets.