Year: 2025
Type: preprint
Abstract: Let $G$ be a permutation group, and denote with $μ(G)$ and $b(G)$ its minimal degree and base size respectively. We show that for every $\varepsilon>0$, there exists a transitive permutation group $G$ of degree $n$ with \[ μ(G)b(G) \geq n^{2-\varepsilon}. \] We also identify some classes of transitive and intransitive groups whose base size and minimal degree have a smaller upper bound, shared with primitive groups.
Source: arXiv (Cornell University)
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979364783
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