Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 7 2 2022 09 01 Some Results on Isologism of Pairs of Groups 209 217 329 10.22128/gadm.2022.623.1080 EN Homayoon Arabyani Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran. Journal Article 2022 10 13 Let ν be a variety of groups defined by a set <em>V</em> of laws. Then the verbal subgroup and the marginal subgroup of a group <em>G</em> associated with the variety are denoted by <em>V (G)</em> and <em>V^∗(G)</em>, respectively. Let (<em>N, G</em>) be a pair of groups in which <em>N</em> is a normal subgroup of <em>G</em>. In the paper, we study the lower and upper ν-marginal series of the pair (<em>N, G</em>) and prove some properties of isologism of pairs of groups. https://ansne.du.ac.ir/article_329_27df04ce1260e9d6c2cab718de068f44.pdf