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Let F be an infinite field of characteristic different from 2 and G a group with involution. Extending the involution to FG, we classify the group rings whose units satisfy a \(*\) -group identity (which, in particular, must occur if the units symmetric with respect to the involution satisfy a group identity). If G is not torsion, some restrictions are required.

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Symmetric Units and \(*\) -Identities

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  • 发表日期：

    2025年

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  • Gregory T. Lee

摘要

Let F be an infinite field of characteristic different from 2 and G a group with involution. Extending the involution to FG, we classify the group rings whose units satisfy a \(*\) -group identity (which, in particular, must occur if the units symmetric with respect to the involution satisfy a group identity). If G is not torsion, some restrictions are required.