Abstract
Let F be an infinite field of characteristic different from 2 and G a group. We examine the set of units, \({\mathcal{U}}^{+}(FG)\), symmetric under the natural involution ∗ sending each group element to its inverse. The conditions under which \({\mathcal{U}}^{+}(FG)\) satisfies a group identity are presented, subject to the restriction 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 Symmetric Units. 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_2
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DOI: https://doi.org/10.1007/978-1-84996-504-0_2
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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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