Normalizers of subgroups of division rings
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B. A. F. Wehrfritz
Abstract
We make a detailed study of the structure of the normalizer of a locally nilpotent subgroup in the multiplicative group of an arbitrary division ring. This generalizes work on nilpotent such subgroups of class 2 dealt with in M. Shirvani's paper [M. Shirvani. On soluble-by-finite subgroups of division algebras. J. Algebra294 (2005), 255–277.] and the author's paper [B. A. F. Wehrfritz. Normalizers of nilpotent subgroups of division rings. Quart. J. Math., to appear.]. For the reasons for doing this, see [M. Shirvani. On soluble-by-finite subgroups of division algebras. J. Algebra294 (2005), 255–277.] and [B. A. F. Wehrfritz. Normalizers of nilpotent subgroups of division rings. Quart. J. Math., to appear.] and references there.
© de Gruyter 2008
Articles in the same Issue
- Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents
- Involution models of finite Coxeter groups
- Prime divisors of character degrees
- A characterization of HN
- Symmetric groups and conjugacy classes
- Conjugacy classes of non-normal subgroups in finite nilpotent groups
- Normalizers of subgroups of division rings
- On the Frattini and upper near Frattini subgroups of a generalized free product
- Reflection principle characterizing groups in which unconditionally closed sets are algebraic
Articles in the same Issue
- Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents
- Involution models of finite Coxeter groups
- Prime divisors of character degrees
- A characterization of HN
- Symmetric groups and conjugacy classes
- Conjugacy classes of non-normal subgroups in finite nilpotent groups
- Normalizers of subgroups of division rings
- On the Frattini and upper near Frattini subgroups of a generalized free product
- Reflection principle characterizing groups in which unconditionally closed sets are algebraic
