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arXiv · 1704.08214

Nilpotency and the number of word maps of a finite group

Alexander Bors
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Abstract

For a finite group $G$ and a non-negative integer $d$, denote by $\Omega_d(G)$ the number of functions $G^d\rightarrow G$ that are induced by substitution into a word with variables among $X_1,\ldots,X_d$. In this note, we show that nilpotency of $G$ can be characterized through the asymptotic growth rate of $\Omega_d(G)$ as $d\to\infty$.

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Alexander Bors. 2017-04-26. Nilpotency and the number of word maps of a finite group. https://arxiv.org/abs/1704.08214

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