Another criterion for solvability of finite groups

@article{Herzog2021AnotherCF,
  title={Another criterion for solvability of finite groups},
  author={Marcel Herzog and Patrizia Longobardi and Mercede Maj},
  journal={Journal of Algebra},
  year={2021}
}

NEW CRITERIA FOR SOLVABILITY, NILPOTENCY AND OTHER PROPERTIES OF FINITE GROUPS IN TERMS OF THE ORDER ELEMENTS OR SUBGROUPS

. In this survey we shall describe some recent criteria for solvability, nilpotency and other properties of finite groups G , based either on the orders of the elements of G or on the orders of the

On the sum of the inverses of the element orders in finite groups

Abstract Let G be a finite group. Recently various functions are defined related to the set of order elements of G and using these functions, some interesting criteria for solvability, nilpotency,

The solvability of a finite group by the sum of powers of element orders

We prove a new criterion for the solvability of the finite groups, depending on the function ψ k ( G ) which is defined as the sum of k -th powers of the element orders of G . We show that our result

On the average order of a finite group

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