The problem of spectra of solvability for varieties of algebras (Q805647)

Let V be a variety of algebras, X be a subvariety of V. The S-spectrum of X in V is the class of all ordinal numbers which occur as steps of X- solvability (in the sense of \textit{L. N. Shevrin} and the author [Sib. Mat. Zh. 12, 1363-1381 (1971; Zbl 0233.08004)]) of some algebras from V. The problem of S-spectra for V consists in the following: find the S- spectra of all subvarieties of V. In this paper, sufficient conditions for the S-spectrum X in V to be unbounded are found. Using this, the problem of S-spectra is decided for some varieties of modules, all varieties of unars, and all varieties of solvable groups; all S-spectra are either finite or coincide with the class of all ordinal numbers.