ON THE LAWS OF FINITE DIHEDRAL POINTED-GROUPS

Abstract

A pointed-group is a pair (G, c) consisting of a group G together with a special element c of G. We call G the carrier of (G, c) and c the focus of (G, c) Oates and Powell6 proved a well-known theorem which states that the variety generated by any finite group is finitely based i.e. there is a finite set of laws of which every laws of a group is a consequence. The aim of this paper is to examine a partial generalization of the Oates and Powell result. Thus we consider analogous statement for dihedral pointed-groups (G, c) only where G is a dihedral group of order 6 and c ranges over the elements of G. However, tables are given showing the basis of finite pointed-groups whose carrier is the dihedral group of order 2n for n≥3.