Detecting structural properties of finite groups by the sum of element orders

DOI10.1007/s11856-020-2033-9zbMath1483.20048arXiv1904.03340OpenAlexW3038762484MaRDI QIDQ2200052

Marius Tărnăuceanu

Publication date: 15 September 2020

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.03340

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60)

Related Items (14)

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 ⋮ An answer to a conjecture on the sum of element orders ⋮ On two conjectures about the sum of element orders ⋮ 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 ⋮ On groups with average element orders equal to the average order of the alternating group of degree \(5\) ⋮ An exact upper bound for the sum of powers of element orders in non-cyclic finite groups ⋮ A criterion for p-nilpotency and p-closedness by the sum of element orders ⋮ Unnamed Item ⋮ PROPERTIES OF FINITE GROUPS DETERMINED BY THE PRODUCT OF THEIR ELEMENT ORDERS ⋮ A generalization of a result on the sum of element orders of a finite group ⋮ On the average order of a finite group

Cites Work

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• A nilpotency criterion for finite groups
• Two new criteria for solvability of finite groups
• An exact upper bound for sums of element orders in non-cyclic finite groups
• A criterion for solvability of a finite group by the sum of element orders
• Second Maximum Sum of Element Orders of Finite Nilpotent Groups
• SUM OF ELEMENT ORDERS ON FINITE GROUPS OF THE SAME ORDER
• Sums of Element Orders in Finite Groups
• Sums of element orders in groups of order 2m with m odd
• On Groups with the Second Largest Value of the Sum of Element Orders

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