Upper bounds for the product of element orders of finite groups

Upper bounds for the product of element orders of finite groups

Let G be a finite group of order n , and denote by ρ ( G ) the product of element orders of G . The aim of this work is to provide some upper bounds for ρ ( G ) depending only on n and on its least prime divisor, when G belongs to some classes of non-cyclic groups.

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Veröffentlicht in:Journal of algebraic combinatorics 2023-06, Vol.57 (4), p.1033-1043
Hauptverfasser: Di Domenico, Elena, Monetta, Carmine, Noce, Marialaura
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Computer Science
Convex and Discrete Geometry
Group theory
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Upper bounds
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Zusammenfassung:Let G be a finite group of order n , and denote by ρ ( G ) the product of element orders of G . The aim of this work is to provide some upper bounds for ρ ( G ) depending only on n and on its least prime divisor, when G belongs to some classes of non-cyclic groups.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-023-01222-w