Profinite just infinite residually solvable Lie algebras

Document Type : Research Paper

Author

Department of Mathematics and Computer Science “U. Dini”, Università degli Studi di Firenze, viale Morgagni 67/A, 50134, Florence, Italy

Abstract

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.

Keywords

Main Subjects

References

[1] C. D. Reid, On the structure of just infinite profinite groups, J. Algebra, 324 (2010) 2249–2261.
[2] C. D. Reid, Inverse system characterizations of the (hereditarily) just infinite property in profinite groups, Bull.
Lond. Math. Soc., 44 (2012) 413-425.
International Journal of Group Theory
Volume 12, Issue 4 - Serial Number 4
December 2023
Pages 253-264

Files

History

  • Receive Date: 14 August 2021
  • Revise Date: 12 July 2022
  • Accept Date: 13 July 2022
  • Published Online: 01 December 2023

Share

How to cite

Statistics