On the average order of a finite group

DOI10.1016/j.jpaa.2022.107276OpenAlexW4308981367MaRDI QIDQ2104900

Marius Tărnăuceanu, Mihai-Silviu Lazorec

Publication date: 8 December 2022

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

Full work available at URL: https://arxiv.org/abs/2210.16666

zbMATH Keywords

solvable groupselementary abelian groupsgroup element ordersaverage order of a group

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Solvable groups, supersolvable groups (20F16) Finite nilpotent groups, (p)-groups (20D15)

Related Items (1)

On groups with average element orders equal to the average order of the alternating group of degree \(5\)

Uses Software

• GAP

Cites Work

• On the number of conjugacy classes of finite nilpotent groups.
• Nonsolvable groups with an automorphism inverting many elements
• 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
• Another criterion for solvability of finite groups
• Detecting structural properties of finite groups by the sum of element orders
• The second maximal groups with respect to the sum of element orders
• The average element order and the number of conjugacy classes of finite groups
• SUM OF ELEMENT ORDERS ON FINITE GROUPS OF THE SAME ORDER
• An arithmetic method of counting the subgroups of a finite abelian group
• Sums of Element Orders in Finite Groups
• On two conjectures about the sum of element orders
• A criterion for nilpotency of a finite group by the sum of element orders

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