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Nilpotent subgroups of finite‐dimensional division algebras
Author(s) -
Wehrfritz B. A. F.
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm001
Subject(s) - mathematics , division ring , nilpotent , division (mathematics) , multiplicative function , multiplicative group , prime (order theory) , pure mathematics , focus (optics) , ring (chemistry) , degree (music) , group (periodic table) , algebra over a field , combinatorics , discrete mathematics , arithmetic , mathematical analysis , physics , chemistry , organic chemistry , acoustics , optics
Let D be a division ring of finite degree d and suppose that G is a nilpotent subgroup of the multiplicative group D * of D . We determine the structure of G in terms of d . We produce examples showing that our results are close to the best possible. Our descriptions focus mainly on the centre factor group and the derived subgroup of G . The results are uniform except for some anomalies caused by the prime 2.