University of Isfahan International Journal of Group Theory 2251-7650 12 4 2023 12 01 Profinite just infinite residually solvable Lie algebras 253 264 26772 10.22108/ijgt.2022.130053.1734 EN Dario Villanis Ziani Department of Mathematics and Computer Science “U. Dini”, Università degli Studi di Firenze, viale Morgagni 67/A, 50134, Florence, Italy Journal Article 2021 08 14 We provide some characterization theorems about just infinite profinite residually solvable Lie algebras, similarly to what C. Reid has done for just infinite profinite groups. In particular, we prove that a profinite residually solvable Lie algebra is just infinite if and only if its obliquity subalgebra has finite codimension in the Lie algebra, and we establish a criterion for a profinite residually solvable Lie algebra to be just infinite, looking at the finite Lie algebras occurring in the inverse system. just-infinite Lie algebras profinite Lie algebras residually solvable Lie algebras https://ijgt.ui.ac.ir/article_26772_2b33a31566f445730af689d7f9c7233b.pdf