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Chain Conditions for Abelian Normal Subgroups
Abstract
We investigate various chain conditions for abelian normal subgroups of groups, following Robinson (1968). We focus on the maximal condition for abelian normal subgroups, an exceptional case excluded from his results except for some counterexamples. In particular we show that a hypercentral group satisfies the maximal condition for abelian normal subgroups if and only if it is is finitely generated nilpotent.
Related
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BibTeX
@misc{aldosray2026chain,
title = {{Chain Conditions for Abelian Normal Subgroups}},
author = {Falih A. M. Aldosray and Ian Stewart},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01964},
eprint = {2611.01964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01964},
}
RIS
TY - UNPB
TI - Chain Conditions for Abelian Normal Subgroups
AU - Falih A. M. Aldosray
AU - Ian Stewart
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01964
UR - https://arxiv.org/abs/2611.01964
AB - We investigate various chain conditions for abelian normal subgroups of groups, following Robinson (1968). We focus on the maximal condition for abelian normal subgroups, an exceptional case excluded from his results except for some counterexamples. In particular we show that a hypercentral group satisfies the maximal condition for abelian normal subgroups if and only if it is is finitely generated nilpotent.
ER -