On a new product of groups
A new product of groups, the rotary product, is introduced: Let \(G\) be a group, Sym\((G)\) the group of all permutations on \(G\) and Sym\(_ e(G)\) the stabilizer of the identity \(e\in G\) in Sym\((G)\). A subgroup \(H\) of Sym\(_ e(G)\) is called rotary closed provided that \(L_{\phi(g)^{- 1}}\phi L_ g\psi\in H\) for all \(\phi,\psi\in H\) and \(g\in G\), where \(L_{\phi(g)^{-1}}\), \(L_ g\in\text{Sym}(G)\) are left multiplications by the elements \(\phi(g)^{-1}\) and \(g\), respectively. For a group \(G\) and a rotary closed subgroup \(H\) of Sym\(_ e(G)\) the rotary product \(G\odot H\) is defined to be the set \(G\times H\) together with the multiplication \((g,\phi)\cdot(f,\psi)=(g\cdot\phi(f),\phi\odot_ g\psi)\).
scientific article; zbMATH DE number 597750