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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbf{F}\)</EquationSource> </InlineEquation> be a field of characteristic different from 2, <i>G</i> a group and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbf{F}G\)</EquationSource> </InlineEquation> its group algebra. In this manuscript, we survey the most relevant results involving group identities satisfied by the subgroup of unitary units. We discuss past and recent developments concerning Cayley unitary elements of the group algebra <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbf{F}G\)</EquationSource> </InlineEquation> and we give examples to review the consequences of the studied results. Furthermore, we formulate some problems that can be boarded in future works.</p>

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Unitary units & Cayley unitary elements in group algebras

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Alexander Holguín-Villa,
  • John H. Castillo

摘要

Let \(\mathbf{F}\) be a field of characteristic different from 2, G a group and \(\mathbf{F}G\) its group algebra. In this manuscript, we survey the most relevant results involving group identities satisfied by the subgroup of unitary units. We discuss past and recent developments concerning Cayley unitary elements of the group algebra \(\mathbf{F}G\) and we give examples to review the consequences of the studied results. Furthermore, we formulate some problems that can be boarded in future works.