Year: 2026
Type: preprint
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 $S_4$ and $C_2^4\rtimes D_{10}$. 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 $|G|$.
Source: arXiv (Cornell University)
Author: Kato, Julia
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G8285809817
OpenAlex ID: W7215679692