New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups

DOI10.22108/ijgt.2022.131888.1766OpenAlexW4376508366MaRDI QIDQ5872404

Patrizia Longobardi, Marcel Herzog, Mercede Maj

Publication date: 30 January 2023

Full work available at URL: https://doaj.org/article/322fd91f99a54d0c8d71263067b4ed71

zbMATH Keywords

solvabilitynilpotencyelement orders

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Solvable groups, supersolvable groups (20F16) Nilpotent groups (20F18)

Related Items (3)

On groups with average element orders equal to the average order of the alternating group of degree \(5\) ⋮ Upper bounds for the product of element orders of finite groups ⋮ Some density results involving the average order of a finite group

Cites Work

• Unnamed Item
• A sufficient condition for nilpotency of the commutator subgroup
• On the number of conjugacy classes of finite nilpotent groups.
• A criterion for metanilpotency of a finite group
• 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
• A proof of Szep's conjecture on nonsimplicity of certain finite groups
• On the number of cyclic subgroups of a finite group
• A density result on the sum of element orders of a finite group
• Detecting structural properties of finite groups by the sum of element orders
• The average element order and the number of conjugacy classes of finite groups
• A result on the number of cyclic subgroups of a finite group
• A result on the sum of element orders of a finite group
• Finite groups determined by an inequality of the orders of their subgroups.
• Inequalities detecting structural properties of a finite group
• Sums of Element Orders in Finite Groups
• Finite groups determined by an inequality of the orders of their subgroups II
• On the solvability of a finite group by the sum of subgroup orders
• Coprime commutators in finite groups
• Sums of element orders in groups of order 2m with m odd
• A NILPOTENCY CRITERION FOR SOME VERBAL SUBGROUPS
• A criterion for nilpotency of a finite group by the sum of element orders
• On a criterion for solvability of a finite group

This page was built for publication: New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups