PreprintCC0arXiv
Finite Non-p-Groups with 5 Automorphism Orbits
Abstract
We obtain a characterization of finite non-p-groups with five automorphism orbits. In the solvable case of Fitting height $3$, the groups are precisely S4 and C24rtimes D10. Moreover, the corresponding fixed-point subspaces form a spread in a finite projective space. For Fitting height $2$, we distinguish the possible structures according to the number of prime divisors of |G|.
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BibTeX
@misc{kato2026finite,
title = {{Finite Non-$p$-Groups with 5 Automorphism Orbits}},
author = {Julia Kato},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00786},
eprint = {2610.00786},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00786},
note = {CC0},
}
RIS
TY - UNPB
TI - Finite Non-p-Groups with 5 Automorphism Orbits
AU - Julia Kato
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00786
UR - https://arxiv.org/abs/2610.00786
AB - We obtain a characterization of finite non-p-groups with five automorphism orbits. In the solvable case of Fitting height $3$, the groups are precisely S_4 and C_2^4rtimes D_10. Moreover, the corresponding fixed-point subspaces form a spread in a finite projective space. For Fitting height $2$, we distinguish the possible structures according to the number of prime divisors of |G|.
ER -