S.A.Adeleke, M.A.E.Dummett and P.M.Neumann remarked in [1] that the notion of a semilinearly ordered group was presented in 1903 by G.Frege in [2]. This notation was introduced in connection with the question on the minimality and independence of an axiom system for the field of real numbers. The problem whether there exists a semilinear-ordered group which is not a right-ordered group has been open for a long time. The first example of a proper semilinearly ordered group was presented in [1] at 1987. In this work the authors derive some properties of semilinearly ordered groups. The paper [1] is the ”starting point” for a study of semilinearly ordered groups.