Datuashvili, TamarŞahan, Tunçar2023-01-132023-01-1320231072-947Xhttps:/dx.doi.org/10.1515/gmj-2022-2205https://hdl.handle.net/20.500.12451/9911A notion of pentaction of any object in the category rGr .{\mathbf{rGr}^{\bullet}} of reduced groups with action is introduced. The operations are defined in the set »e - - ac - (A) {\mathsf{Pentact}(A)} of pentactions of an object A of rGr.{\mathbf{rGr}^{\bullet}}. It is proved that if an object A is perfect with zero weak stabilizer in the sense defined in this paper, then »e-ac-(A) {\mathsf{Pentact}(A)} is an object of rGr. {\mathbf{rGr}^{\bullet}}, it has a derived action on A, the object A is action representable and »e - - ac -(A) {\mathsf{Pentact}(A)} represents all actions on A.eninfo:eu-repo/semantics/openAccessAction RepresentabilityGroup with ActionPentactionArticle----10.1515/gmj-2022-2205Q2WOS:000892350600001Q3