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.
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