Engel identity
The Engel identity, named after Friedrich Engel, is a mathematical equation that is satisfied by all elements of a Lie ring, in the case of an Engel Lie ring, or by all the elements of a group, in the case of an Engel group. The Engel identity is the defining condition of an Engel group.A Lie ring is defined as a nonassociative ring with multiplication that is anticommutative and satisfies the Jacobi identity with respect to the Lie bracket, defined for all elements in the ring. The Lie ring is defined to be an n-Engel Lie ring if and only if
- for all in, the n-Engel identity
, is satisfied.
In the case of a group, in the preceding definition, use the definition and replace by, where is the identity element of the group.
