Strongly not divisible Abelian groups

Abstract An Abelian group 𝐺 is called strongly not divisible if <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>⁢</m:mo> <m:mi>G</m:mi> </m:mrow> <m:mo>≠</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> nG\neq G for every integer <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>≠</m:mo> <m:mrow> <m:mo>±</m:mo> <m:mn>1</m:mn> </m:mrow> </m:mrow> </m:math> n\neq\pm 1 . In J. A. Lewallen and N. Sagullo, A note on OI torsion abelian groups, Missouri J. Math. Sci. 27 (2015), 1, 33–36, a characterization of the torsion strongly not divisible groups (referred to there as OI-groups) was obtained. In this note, we provide characterizations for broad classes of torsion-free and mixed strongly not divisible groups.