English

Locally solvable and solvable-by-finite maximal subgroups of $GL_n(D)$

Rings and Algebras 2021-12-21 v4

Abstract

This paper aims at studying solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup of the general skew linear group \GLn(D)\GL_n(D) over a division ring DD. It turns out that in the case where DD is non-commutative, if such maximal subgroups exist, then either it is abelian or [D:F]<[D:F]<\infty. Also, if FF is an infinite field and n5n\geq 5, then every locally solvable maximal subgroup of a normal subgroup of \GLn(F)\GL_n(F) is abelian.

Keywords

Cite

@article{arxiv.1903.10868,
  title  = {Locally solvable and solvable-by-finite maximal subgroups of $GL_n(D)$},
  author = {Huynh Viet Khanh and Bui Xuan Hai},
  journal= {arXiv preprint arXiv:1903.10868},
  year   = {2021}
}

Comments

Accepted for publication in Publicacions Matem\`atiques (UAB)