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Free Subgroups in Maximal Subgroups of GL1(D)

✍ Scribed by M Mahdavi-Hezavehi

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
94 KB
Volume
241
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let D be a division algebra of finite dimension over its center F. Given a Ε½ . noncommutative maximal subgroup M of D* [ GL D , it is proved that either 1 M contains a noncyclic free subgroup or there exists a maximal subfield K of D Ε½ . which is Galois over F such that K * is normal in M and MrK * ( Gal KrF . Using this result, it is shown in particular that if D is a noncrossed product division algebra, then M does not satisfy any group identity.

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