Hall–Petresco Identity

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
:$x^my^m=(xy)^mc_2^c_3^\cdots c_^c_m$
where each ''c''_''i'' is in the subgroup ''K''_''i'' of the descending central series of ''G''.

See also

* Baker–Campbell–Hausdorff formula
* Algebra of symbols

References

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{{DEFAULTSORT:Hall-Petresco identity
P-groups
Combinatorial group theory