PreprintCC BY-NC-ND 4.0arXiv
Abelian quotients and orbit sizes for subgroups of linear groups
Abstract
Keller and Yang formulated two conjectures relating abelian quotients of subgroups of finite linear groups to largest orbit sizes. After counterexamples were found to the original conjectures, two revised versions were proposed. We prove both revised conjectures for every finite group G satisfying F(G)=F*(G). We also extend a regular-orbit theorem for nilpotent subgroups to completely reducible modules of mixed characteristic under the same hypothesis.
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BibTeX
@misc{yang2026abelian,
title = {{Abelian quotients and orbit sizes for subgroups of linear groups}},
author = {Yong Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34680},
eprint = {2610.34680},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34680},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Abelian quotients and orbit sizes for subgroups of linear groups
AU - Yong Yang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34680
UR - https://arxiv.org/abs/2610.34680
AB - Keller and Yang formulated two conjectures relating abelian quotients of subgroups of finite linear groups to largest orbit sizes. After counterexamples were found to the original conjectures, two revised versions were proposed. We prove both revised conjectures for every finite group G satisfying F(G)=F^*(G). We also extend a regular-orbit theorem for nilpotent subgroups to completely reducible modules of mixed characteristic under the same hypothesis.
ER -