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• W2031079741 abstract "Let M m ( D ) be a finite dimensional F -central simple algebra. It is shown that M m ( D ) is a crossed product over a maximal subfield if and only if GL m ( D ) has an irreducible subgroup G containing a normal abelian subgroup A such that C G ( 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 deg ( D ) 2 , then D is a crossed product over a maximal subfield." @default.
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• W2031079741 date "2007-09-01" @default.
• W2031079741 modified "2023-09-29" @default.
• W2031079741 title "Crossed product conditions for central simple algebras in terms of irreducible subgroups" @default.
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• W2031079741 doi "https://doi.org/10.1016/j.jalgebra.2007.05.002" @default.
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