Locally solvable maximal subgroups in division rings · arXivDesk
1908.04925Aug 14, 2019This version[v3] was accepted for publication in Kyoto Journal of Mathematics in 2022. Comparing to the version v2, the title of the paper has been changed and some theorems were renumbered. The version v2 was entitled "On almost subnormal subgroups in division rings". Also, the two main results Theorems 3.10 and 3.11 in v2 were renumbered as Theorems 1.1 and 1.2 in the accepted version v3
Locally solvable maximal subgroups in division rings
Let D be a division ring with center F, and G an almost subnormal subgroup of D∗. In this paper, we show that if G contains a non-abelian locally solvable maximal subgroup, then D
Nearby in the stack
must be a cyclic algebra of prime degree over
F
. Moreover, it is proved that every locally nilpotent maximal subgroup of