However it was not until the late 1930s and early 1940s that the study of semigroups became a major topic. Malcev, Clifford and Dubreil became major figures in the new subject, Dubreil's first major work being Contribution à la théorie des demi-groupes.
Gayunpaman, ito ay hindi hanggang sa late 1930s at unang bahagi ng 1940s na ang pag-aaral ng semigroups ay naging isang pangunahing paksa. Malcev, Clifford at Dubreil naging pangunahing numero sa mga bagong paksa, Dubreil ng unang malaking trabaho na kontribusyon ŕ la théorie des demi-groupes.