In mathematics, the Hall–Petresco identity (sometimes misspelled Hall–Petrescu identity) is an identity holding in any group. It was introduced by and . It can be proved using the commutator collecting process, and implies that p-groups of small class are regular.
Statement
The Hall–Petresco identity states that if x and y are elements of a group G and m is a positive integer then
where each ci is in the subgroup Ki of the descending central series of G.
See also Baker–Campbell–Hausdorff formula Algebra of symbols
References