Two characterizations of the smallest non-solvable group (Q6636335)

The paper provides two characterizations of the smallest non-abelian simple group \(A_{5}\). However, the authors introduce two functions which are more difficult to visualize than the well-known alternating group of degree~\(5\). Instead of defining the functions with derivatives and integrals, one could use their values evaluated at \(1\), which still seem more group theoretical. The authors end with an open problem of a characterization of similar nature, derived from a technical formula, deduced by GAP computations.