Lie rings are used in the study of finite p-groups (for a prime number p) through the Lazard correspondence. The lower central factors of a finite p-group are finite abelian p-groups. The direct sum of the lower central factors is given the structure of a Lie ring by defining the bracket to be the commutator of two coset representatives; see the example below.
Lie rings are used in the study of finite p-groups (for a prime number p) through the Lazard correspondence The lower central factors of a finite p-group are finite abelian p-groups The direct sum of the lower central factors is given the structure of a Lie ring by defining the bracket to be the commutator of two coset representatives; see the example below