Links for the birthday of the late mathematician Bernhard H. Neumann:
Variety (Universal Algebra) at Wikipedia
Preface to Varieties of Groups (1967), by Hanna Neumann
Some related notes on algebra suggested by finite geometry:
Dynamic and algebraic compatibility of groups (1985 Dec. 11)
Groups related by a nontrivial identity (1985 Nov. 17)
Transformations over a bridge (1983 Aug. 16)
Group identity algebras (1983 Aug. 4)
I have no idea if any work has been done in this area since my own efforts in 1983-1985.