The second maximal groups with respect to the sum of element orders

DOI10.1016/j.jpaa.2020.106531zbMath1462.20011arXiv1901.09662OpenAlexW3073717275MaRDI QIDQ2200952

Mercede Maj, Marcel Herzog, Patrizia Longobardi

Publication date: 24 September 2020

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

Full work available at URL: https://arxiv.org/abs/1901.09662

zbMATH Keywords

finite groupsgroup element orders

Mathematics Subject Classification ID

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

Related Items (12)

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 ⋮ 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 ⋮ PROPERTIES OF FINITE GROUPS DETERMINED BY THE PRODUCT OF THEIR ELEMENT ORDERS ⋮ Sums of element orders in groups of odd order ⋮ A generalization of a result on the sum of element orders of a finite group ⋮ 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

• Second maximum sum of element orders on finite groups.
• Maximum sum element orders of all proper subgroups of \(PGL(2,q)\).
• 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
• Sum of the element orders in groups of the square-free orders
• Second Maximum Sum of Element Orders of Finite Nilpotent Groups
• ON THE SUM OF ELEMENT ORDERS OF FINITE SIMPLE GROUPS
• Sum of Element Orders of Maximal Subgroups of the Symmetric Group
• SUM OF ELEMENT ORDERS ON FINITE GROUPS OF THE SAME ORDER
• Sums of Element Orders in Finite Groups
• ON THE SUM OF ELEMENT ORDERS OF FINITE ABELIAN GROUPS
• Characterization of $p$-groups by sum of the element orders
• On Groups with the Second Largest Value of the Sum of Element Orders
• Sum of the Products of the Orders of Two Distinct Elements in Finite Groups

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