Almost subnormal subgroups in division rings with generalized algebraic rational identities

TL;DR

This paper investigates the structure of almost subnormal subgroups in division rings satisfying generalized rational identities, extending existing theorems and providing new insights into their algebraic properties.

Contribution

It generalizes Chiba's theorem on subnormal subgroups and introduces new results on almost subnormal subgroups satisfying generalized algebraic rational identities.

Findings

Generalization of Chiba's theorem

New theorems on almost subnormal subgroups

Several corollaries extending previous results

Abstract

In this paper we study non-central almost subnormal subgroups of the multiplicative group of a division ring satisfying a non-zero generalized rational identity. The main result generalizes Chiba's theorem on subnormal subgroups. As an application, we get a theorem on almost subnormal subgroups satisfying a generalized algebraic rational identity. The last theorem has several corollaries which generalize completely or partially some previous results.