This symmetry has several equivalent characterizations, which lend to the analysis of such algebras.
is called congruence-permutable when each pair of congruences of
[1]: 122 In 1954 Maltsev gave two other conditions that are equivalent to the one given above defining a congruence-permutable variety of algebras.
This initiated the study of congruence-permutable varieties.
The following are equivalent: Such a term is called a Maltsev term and congruence-permutable varieties are also known as Maltsev varieties in his honor.
[1]: 122 Most classical varieties in abstract algebra, such as groups[1]: 123 , rings[1]: 123 , and Lie algebras[citation needed] are congruence-permutable.
Any variety that contains a group operation is congruence-permutable, and the Maltsev term is
[1]: 123 This abstract algebra-related article is a stub.