In mathematics, the Hall–Petresco identity (sometimes misspelled Hall–Petrescu identity) is an identity holding in any group. It was introduced by Hall (1934) and Petresco (1954). 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.
References
Hall–Petresco identity Wikipedia(Text) CC BY-SA