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arXiv · 2610.16241

A non-nilpotent localization of a finite p-group

Sergei O. Ivanov·Georgii Kadantsev
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Abstract

We give negative answers to two questions of Farjoun about localizations of groups. For every odd prime $p$, we construct a finite $p$-group $G$, an infinite non-nilpotent group $H$, and a local embedding $f\colon G\hookrightarrow H$. The associated localization satisfies $L_f(G)\cong H$, showing that localizations need not preserve nilpotence and that the localization map $G\to L(G)$ need not be surjective when $G$ is a finite $p$-group.

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Sergei O. Ivanov, Georgii Kadantsev. 2026-10-12. A non-nilpotent localization of a finite p-group. https://arxiv.org/abs/2610.16241

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