Lexicographic products of half linearly ordered groups

The notion of the half linearly ordered group land, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups. This definition includes as a particular case the lexicographic product of linearly ordered groups. We investigate the problem of the existence of isomorphic refinements of two lexicographic product decompositions of a half linearly ordered group. The analogous problem for linearly ordered groups was dealt with by Maltsev [5]; his result was generalized by Fuchs [1] and the author [3]. The isomorphic refinements of small direct product decompositions of half lattice ordered groups were studied in [4].