Datuashvili, TamarŞahan, Tunçar2023-03-132023-03-1320232651-477Xhttps:/dx.doi.org/10.15672/hujms.1028848https://hdl.handle.net/20.500.12451/10329Derived actions in the category of groups with action on itself Gr• are defined and de-scribed. This category plays a crucial role in the solution of two problems of Loday stated in the literature. A full subcategory of reduced groups with action rGr• of Gr• is intro-duced, which is not a category of interest but has some properties, which can be applied in the investigation of action representability in this category; these properties are similar to those, which were used in the construction of universal strict general actors in the category of interest. Semi-direct product constructions are given in Gr• and rGr• and it is proved that an action is a derived action in Gr• (resp. rGr•) if and only if the corresponding semi-direct product is an object of Gr• (resp. rGr•). The results obtained in this paper will be applied in the forthcoming paper on the representability of actions in the category rGr•.eninfo:eu-repo/semantics/openAccessGroup with ActionSemi-direct ProductActionExtensionArticle52110311310.15672/hujms.1028848Q2WOS:000964265900008Q2