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<p>We study the index and period of powers of periodic elements. Using the Fitting lemma and the exponent of the finite group <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(GL_n(\mathbb F_q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <msub> <mi>L</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, we construct the common index and the common period of the elements of a finite ring.</p>

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Index and Period in Finite Rings

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Guanglin Ma,
  • André Leroy,
  • Chungen Xu

摘要

We study the index and period of powers of periodic elements. Using the Fitting lemma and the exponent of the finite group \(GL_n(\mathbb F_q)\) G L n ( F q ) , we construct the common index and the common period of the elements of a finite ring.