Abstract
Let F be a field and G a group. We consider the unit group, \(\mathcal{U}(FG)\), and ask when it will satisfy a group identity w(x 1, …, x n ) = 1. We present the proof of Hartley’s Conjecture, namely that if \(\mathcal{U}(FG)\) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. We then prove necessary and sufficient conditions for \(\mathcal{U}(FG)\) to satisfy a group identity. (When G is not torsion, we must assume that G ∕ T is a u.p. group for the sufficiency, where T is the set of torsion elements of G.)
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© 2010 Springer London
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Lee, G.T. (2010). Group Identities on Units of Group Rings. In: Group Identities on Units and Symmetric Units of Group Rings. Algebra and Applications, vol 12. Springer, London. https://doi.org/10.1007/978-1-84996-504-0_1
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DOI: https://doi.org/10.1007/978-1-84996-504-0_1
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Publisher Name: Springer, London
Print ISBN: 978-1-84996-503-3
Online ISBN: 978-1-84996-504-0
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