On locally nilpotent maximal subgroups of the multiplicative group of a division ring

Details On locally nilpotent maximal subgroups of the multiplicative group of a division ring On locally nilpotent maximal subgroups of the multiplicative group of a division ring

2009-09-25

arxiv.org/abs/0909.4726v2

Mathematics

Rings and Algebras

Scientific paper

Let $D$ be a division ring with the center $F$ and $D^*$ be the multiplicative group of $D$. In this paper we study locally nilpotent maximal subgroups of $D^*$. We give some conditions that influence the existence of locally nilpotent maximal subgroups in division ring with infinite center. Also, it is shown that if $M$ is a locally nilpotent maximal subgroup that is algebraic over $F$, then either it is the multiplicative group of some maximal subfield of $D$ or it is center by locally finite. If, in addition we assume that $F$ is finite and $M$ is nilpotent, then the second case cannot occur, i.e. $M$ is the multiplicative group of some maximal subfield of $D$.

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