PreprintCC BY 4.0arXiv
On a finite group in which every non-nilpotent maximal invariant subgroup of order divisible by p is normal
Abstract
Let A and G be finite groups such that A acts coprimely on G by automorphisms. For any fixed prime divisor p of |G|, we prove that if every non-nilpotent maximal A-invariant subgroup of G of order divisible by p is normal then G has a Sylow tower and G is q-nilpotent or q-closed for each prime divisor q of |G|.
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BibTeX
@misc{shi2026finite,
title = {{On a finite group in which every non-nilpotent maximal invariant subgroup of order divisible by $p$ is normal}},
author = {Jiangtao Shi and Fanghua Li and Na Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30653},
eprint = {2610.30653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30653},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On a finite group in which every non-nilpotent maximal invariant subgroup of order divisible by p is normal
AU - Jiangtao Shi
AU - Fanghua Li
AU - Na Li
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30653
UR - https://arxiv.org/abs/2610.30653
AB - Let A and G be finite groups such that A acts coprimely on G by automorphisms. For any fixed prime divisor p of |G|, we prove that if every non-nilpotent maximal A-invariant subgroup of G of order divisible by p is normal then G has a Sylow tower and G is q-nilpotent or q-closed for each prime divisor q of |G|.
ER -