a generalization of taketa’s theorem on m-groups ii

In the recent paper [a generalization of taketa’s theorem on mgroups, quaestiones mathematicae, (2022)], we give an upper bound 5/2 for the average of non-monomial character degrees of a finite group g, denoted by acdnm(g), which guarantees the solvability of g. although the result is true, the example we gave to show that the bound is sharp turns out to be incorrect. in this paper we find a new bound and we give an example to show that this new bound is sharp. indeed, we prove the solvability of g, by assuming acdnm(g) < acdnm(sl2(5)) = 19/7.