Article ID Journal Published Year Pages File Type
4588670 Journal of Algebra 2007 7 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory