University of Kashan Mathematics Interdisciplinary Research 2538-3639 5 4 2020 12 01 On Nilpotent Multipliers of Pairs of Groups 367 377 111342 10.22052/mir.2020.240332.1250 EN Azam Hokmabadi Department of Mathematics, Faculty of Sciences, Payame Noor University, 19395-4697 Tehran, I. R. Iran Fahimeh Mohammadzadeh Department of Mathematics, Faculty of Sciences, Payame Noor University, 19395-4697 Tehran, I. R. Iran Behrooz Mashayekhy Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran Journal Article 2020 10 20 In this paper, we determine the structure of the nilpotent multipliers of all pairs (G,N) of finitely generated abelian groups where N admits a complement in G. Moreover, some inequalities for the nilpotent multipliers of pairs of finite groups and their factor groups are given. pair of groups Nilpotent multiplier Finitely generated abelian groups https://mir.kashanu.ac.ir/article_111342_53e46a479d32835bd5501c1cc88bd6b2.pdf