On division subrings normalized by almost subnormal subgroups in division rings

Trinh Thanh Deo; Mai Hoang Bien; Bui Xuan Hai

On division subrings normalized by almost subnormal subgroups in division rings

Rings and Algebras 2019-02-20 v2

Authors: Trinh Thanh Deo , Mai Hoang Bien , Bui Xuan Hai

Abstract

Let $D$ be a division ring with infinite center, $K$ a proper division subring of $D$ and $N$ an almost subnormal subgroup of the multiplicative group $D^*$ of $D$ . The aim of this paper is to show that if $K$ is $N$ -invariant and $N$ is non-central, then $K$ is central. Some examples of almost subnormal subgroups in division rings that are not subnormal are also given.

Keywords

commutative ring theory semigroup theory finite group theory

Cite

@article{arxiv.1801.01271,
  title  = {On division subrings normalized by almost subnormal subgroups in division rings},
  author = {Trinh Thanh Deo and Mai Hoang Bien and Bui Xuan Hai},
  journal= {arXiv preprint arXiv:1801.01271},
  year   = {2019}
}

Comments

13 pages

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