An exact upper bound for sums of element orders in non-cyclic finite groups

DOI10.1016/J.JPAA.2017.07.015zbMath1486.20030arXiv1610.03669OpenAlexW2734391510MaRDI QIDQ1703581

Mercede Maj, Patrizia Longobardi, Marcel Herzog

Publication date: 2 March 2018

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.03669

zbMATH Keywords

sums of element ordersexact upper boundnon-cyclic finite groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Solvable groups, supersolvable groups (20F16) General structure theorems for groups (20E34)

Related Items (33)

On the sum of the inverses of the element orders in finite groups ⋮ Another criterion for supersolvability of finite groups ⋮ The sum of orders of elements in nonabelian groups of odd order ⋮ The minimum sum of element orders of finite groups ⋮ An answer to a conjecture on the sum of element orders ⋮ On two conjectures about the sum of element orders ⋮ Two new criteria for solvability of finite groups ⋮ New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups ⋮ A density result on the sum of element orders of a finite group ⋮ Subgroups with a small sum of element orders ⋮ Addendum to ``A generalization of a result on the sum of element orders of a finite group ⋮ On groups with average element orders equal to the average order of the alternating group of degree \(5\) ⋮ On the sum of orders of elements in finite groups ⋮ Upper bounds for the product of element orders of finite groups ⋮ Detecting structural properties of finite groups by the sum of element orders ⋮ An exact upper bound for the sum of powers of element orders in non-cyclic finite groups ⋮ Unnamed Item ⋮ The second maximal groups with respect to the sum of element orders ⋮ A criterion for p-nilpotency and p-closedness by the sum of element orders ⋮ Unnamed Item ⋮ Unnamed Item ⋮ PROPERTIES OF FINITE GROUPS DETERMINED BY THE PRODUCT OF THEIR ELEMENT ORDERS ⋮ On a divisibility property involving the sum of element orders ⋮ A result on the sum of element orders of a finite group ⋮ Sums of element orders in groups of odd order ⋮ A criterion for solvability of a finite group by the sum of element orders ⋮ A generalization of a result on the sum of element orders of a finite group ⋮ Recognition by the product element orders ⋮ Sums of element orders in groups of order 2m with m odd ⋮ Another criterion for solvability of finite groups ⋮ A criterion for nilpotency of a finite group by the sum of element orders ⋮ On a criterion for solvability of a finite group ⋮ On the average order of a finite group

Cites Work

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• Second maximum sum of element orders on finite groups.
• Second Maximum Sum of Element Orders of Finite Nilpotent Groups
• Inequalities detecting structural properties of a finite group
• SUM OF ELEMENT ORDERS ON FINITE GROUPS OF THE SAME ORDER
• A Remark on Finite Groups
• Sums of Element Orders in Finite Groups
• On Groups with the Second Largest Value of the Sum of Element Orders

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