PreprintCC BY 4.0arXiv
A non-nilpotent localization of a finite p-group
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: G↪ H. The associated localization satisfies Lf(G)≅ H, showing that localizations need not preserve nilpotence and that the localization map G→ L(G) need not be surjective when G is a finite p-group.
Related
- Root vector localization and minimal nilpotent finite W-algebras
- On a finite group in which every maximal subgroup of order divisible by p containing the normalizer of some Sylow subgroup is nilpotent
- On a finite group in which every non-nilpotent maximal invariant subgroup of order divisible by p is normal
- Finite group actions on the non-minimal nilpotent orbit closures in type A
- Orbits of p-Nilpotent Group Actions for Small Primes
BibTeX
@misc{ivanov2026nonnilpotent,
title = {{A non-nilpotent localization of a finite p-group}},
author = {Sergei O. Ivanov and Georgii Kadantsev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16241},
eprint = {2610.16241},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16241},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A non-nilpotent localization of a finite p-group
AU - Sergei O. Ivanov
AU - Georgii Kadantsev
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16241
UR - https://arxiv.org/abs/2610.16241
AB - 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: G↪ H. The associated localization satisfies L_f(G)≅ H, showing that localizations need not preserve nilpotence and that the localization map G→ L(G) need not be surjective when G is a finite p-group.
ER -