Given a finite group R, we let Sub(R) denote the collection of all subgroups of R. We show that [Formula presented], where c<7.372 is an explicit absolute constant. This result is asymptotically best possible. Indeed, as |R| tends to infinity and R is an elementary abelian 2-group, the ratio [Formula presented] tends to c.

Fusari, M., Spiga, P. (2023). On the maximum number of subgroups of a finite group. JOURNAL OF ALGEBRA, 635(1 December 2023), 486-526 [10.1016/j.jalgebra.2023.07.047].

On the maximum number of subgroups of a finite group

Spiga P.
2023

Abstract

Given a finite group R, we let Sub(R) denote the collection of all subgroups of R. We show that [Formula presented], where c<7.372 is an explicit absolute constant. This result is asymptotically best possible. Indeed, as |R| tends to infinity and R is an elementary abelian 2-group, the ratio [Formula presented] tends to c.
Articolo in rivista - Articolo scientifico
Number subgroups; Subgroup lattice; Upper bound;
English
28-ago-2023
2023
635
1 December 2023
486
526
open
Fusari, M., Spiga, P. (2023). On the maximum number of subgroups of a finite group. JOURNAL OF ALGEBRA, 635(1 December 2023), 486-526 [10.1016/j.jalgebra.2023.07.047].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/470960
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