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<p>In the situation where a finite group <i>A</i> acts coprimely by automorphisms on another finite group <i>G</i>, we characterize when the principal <i>p</i>-block of <i>G</i> contains a unique <i>A</i>-invariant irreducible character, in terms of the subgroup <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{C}_{G}(A)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">C</mi> <mi>G</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of fixed points under such action.</p>

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Coprime action and principal blocks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月27日

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  • Zhicheng Feng,
  • Carolina Vallejo

摘要

In the situation where a finite group A acts coprimely by automorphisms on another finite group G, we characterize when the principal p-block of G contains a unique A-invariant irreducible character, in terms of the subgroup \(\textbf{C}_{G}(A)\) C G ( A ) of fixed points under such action.