Bitranslations and symmetric nets
Summary: It is known that every class-regular symmetric \((\mu ,m)\)-net is tactical. Also it is known that all \((\mu ,m)\)-nets with \(m=2\) or \(\mu =1\) are tactical. In the work of \textit{A. N. Al-Kenani} and \textit{V. C. Mavron} [J. Lond. Math. Soc., II. Ser. 67, No. 2, 273--288 (2003; Zbl 1042.05020)], it is proved that every symmetric net with \(m=3\) is tactical if and only if it is class regular. In this paper, we construct a \((2,4)\)-net and show that it is class regular and therefore tactical. New necessary and sufficient conditions are given for a symmetric net to admit a nonidentity bitranslation.
scientific article; zbMATH DE number 5816743