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<p>Let <i>F</i>/<i>R</i> be a free presentation of a finite <i>p</i>-group <i>G</i>. In this paper, we provide an upper bound for the order of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma _3(F)/\gamma _3(R,F)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>γ</mi> <mn>3</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <msub> <mi>γ</mi> <mn>3</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mo>,</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, and show that this bound improves some well-known bounds for the order of the 2-nilpotent multiplier of <i>G</i>. We also provide bounds for the order of the 2-nilpotent multiplier of finite <i>p</i>-groups of fixed coclass. Furthermore, we study the triple tensor product, the triple exterior product and the 2-nilpotent multiplier of finite 2-groups of maximal class, and determine which of them are 2-capable.</p>

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On the 2-nilpotent multipliers of p-groups with fixed coclass

  • 期刊论文

  • 发表日期：

    2025年10月9日

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  • S. Hadi Jafari,
  • J. M. Casas

摘要

Let F/R be a free presentation of a finite p-group G. In this paper, we provide an upper bound for the order of \(\gamma _3(F)/\gamma _3(R,F)\) γ 3 ( F ) / γ 3 ( R , F ) , and show that this bound improves some well-known bounds for the order of the 2-nilpotent multiplier of G. We also provide bounds for the order of the 2-nilpotent multiplier of finite p-groups of fixed coclass. Furthermore, we study the triple tensor product, the triple exterior product and the 2-nilpotent multiplier of finite 2-groups of maximal class, and determine which of them are 2-capable.