Lexicographic extensions and $pl$-groups

It is known that a lexicographic extension of an $l$-group by an $l$-group needs not to be an $l$-group. It has been proved in [7] that such extension is a $pl$-group (introduced in [2] and [4]). The purpose of this paper is to show that the class of $pl$-groups is closed with respect to lexicographic extensions.