Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588670 | Journal of Algebra | 2007 | 7 Pages |
Abstract
Let Mm(D) be a finite dimensional F-central simple algebra. It is shown that Mm(D) is a crossed product over a maximal subfield if and only if GLm(D) has an irreducible subgroup G containing a normal abelian subgroup A such that CG(A)=A and F[A] contains no zero divisor. Various other crossed product conditions on subgroups of D∗ are also investigated. In particular, it is shown that if D∗ contains either an irreducible finite subgroup or an irreducible soluble-by-finite subgroup that contains no element of order dividing deg2(D), then D is a crossed product over a maximal subfield.
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