Abstract. We survey results concerning special elements of eight types (modular, lower-modular, upper-modular, distributive, codistributive, standard, costandard and neutral elements) in the lattice of all semigroup varieties and three of its sublattices, namely, the lattices of commutative varieties, of permutative varieties and of overcommutative ones. These results are due to Ježek, McKenzie, Shaprynski?, Volkov and the author. Several open questions are formulated.

DOI: 10.14232/actasm-013-072-0

AMS Subject Classification (1991): 20M07; 08B15

Keyword(s): semigroup, variety, lattice of varieties, commutative variety, overcommutative variety, permutative variety, modular element, lower-modular element, upper-modular element, distributive element, codistributive element, standard element, costandard element, neutral element

Received October 27, 2013, and in revised form April 29, 2014. (Registered under 72/2013.)