On the base size and minimal degree of transitive groups

On the base size and minimal degree of transitive groups Full article

Journal

Journal of Group Theory
ISSN: 1433-5883

Output data

Year: 2026, DOI: 10.1515/jgth-2025-0145

Authors

Guerra Lorenzo ¹ , Maróti Attila ² , Mastrogiacomo Fabio ³ , Skresanov Saveliy V. ⁴ , Spiga Pablo ¹

Affiliations

1	Dipartimento di Matematica Pura e Applicata , University of Milano-Bicocca , Via Cozzi 55, 20126 Milano , Italy
2	Hun-Ren Alfréd Rényi Institute of Mathematics , Reáltanoda Utca 13-15, 1053 , Budapest , Hungary
3	Dipartimento di Matematica “Felice Casorati” , 19001 University of Pavia , Via Ferrata 5, 27100 Pavia , Italy
4	Sobolev Institute of Mathematics , 4 Acad. Koptyug avenue, 630090 Novosibirsk , Russia

Funding (1)

Министерство науки и высшего образования РФ

FWNF-2026-0017

Let G be a permutation group, and denote with µ(G) and b(G) its minimal degree and base size respectively. We show that there exists a universal constant c > 0 such that for infinitely many n there is a transitive permutation group G of degree n with µ(G)b(G) ≥ c·n2. 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.

Guerra L. , Maróti A. , Mastrogiacomo F. , Skresanov S.V. , Spiga P.
On the base size and minimal degree of transitive groups
Journal of Group Theory. 2026. DOI: 10.1515/jgth-2025-0145 WOS OpenAlex

Published online:

May 12, 2026

≡ Web of science:	WOS:001762544800001
≡ OpenAlex:	W7160849099