%0 Journal Article %T On Condition (G-PWP) %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Arabtash, Mostafa %A Golchin, Akbar %A Mohammadzadeh Saany, Hossein %D 2016 %\ 07/01/2016 %V 5 %N 1 %P 55-84 %! On Condition (G-PWP) %K $S$-act %K condition ($PWP$) %K condition ($G$-$PWP$) %R %X Laan in (Ph.D Thesis, Tartu. 1999) introduced the principal weak form of Condition $(P)$ as Condition $(PWP)$ and gave some characterization of monoids by this condition of their acts. In this paper first we introduce Condition (G-PWP), a generalization of Condition $(PWP)$ of acts over monoids and then will give a characterization of monoids when all right acts satisfy this condition. We also give a characterization of monoids, by comparing this property of their acts with some others. Finally, we give a characterization of monoids coming from some special classes, by this property of their diagonal acts and extend some results on Condition $(PWP)$ to this condition of acts. %U https://cgasa.sbu.ac.ir/article_13905_e158b94d9effd3026710c9030d20f056.pdf