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Maximal Subgroups of GL1(D)

✍ Scribed by S. Akbari; M. Mahdavi-Hezavehi; M.G. Mahmudi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
95 KB
Volume
217
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let D be a division algebra of degree m over its center F. Herstein has shown Ε½ . that any finite normal subgroup of D* [ GL D is central. Here, as a generaliza-1 tion of this result, it is shown that any finitely generated normal subgroup of D* is Ε½ central. This also solves a problem raised by Akbari and Mahdavi-Hezavehi Proc.

. Amer. Math. Soc., to appear for finite-dimensional division algebras. The structure of maximal multiplicative subgroups of an arbitrary division ring D is then investigated. Given a maximal subgroup M of D* whose center is algebraic over F, it is proved that if M satisfies a multilinear polynomial identity over F, then w x D : F -Ο±.

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