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<p>Let <i>F</i> be an arbitrary field with more than three elements. In this short note, we show that the commutator width of the Vershik-Kerov group over <i>F</i> is one; that is, every element in its commutator subgroup can be expressed as a single commutator. This result sharpens previously established upper bounds, which only asserted that the commutator width is at most two or three.</p>

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On the commutator width of the Vershik-Kerov group

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Le Quang Truong

摘要

Let F be an arbitrary field with more than three elements. In this short note, we show that the commutator width of the Vershik-Kerov group over F is one; that is, every element in its commutator subgroup can be expressed as a single commutator. This result sharpens previously established upper bounds, which only asserted that the commutator width is at most two or three.