Title: Isomorphism of noncommutative group algebras of torsion-free groups over a field
Abstract: The isomorphism problem for group algebras over a field with arbitrary characteristic of some special classes of torsion-free non-abelian groups is explored. Specifically, the following are proved: Suppose F is a field and G is a torsion-free group with centre C(G) such that FG∼ FH as F-algebras for any group H. Then it is shown that H is torsion-free (provided that FGis without zero divisors), and if G is soluble we have even more that C(G) ∼ C(H). The latter extends classical results due to Higman(1940)-May(1969) when G is torsion-free abelian. Moreover, if G is an R-group or a D-group, then the above Fisomorphism yields that so is H.
Publication Year: 2005
Publication Date: 2005-01-01
Language: en
Type: article
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