The finite basis problem for finite semigroups (Q2740982)

The paper is a survey of recent research on the finite basis problem for finite semigroups. In this respect it is an update of the earlier survey by \textit{L. N. Shevrin} and \textit{M. V. Volkov} [Izv. Vyssh. Uchebn. Zaved., Mat. 1985, No. 11, 3-47 (1985; Zbl 0629.20029)] which dealt more generally with identities of semigroups, but no familiarity with the earlier paper is required to read the present one. The status of open problems proposed in the previous survey as well as new problems are discussed. In particular, the paper includes a very clear presentation and comparison of the methods found in the literature for proving that a finite semigroup is not finitely based.