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Hall–Petresco identity : ウィキペディア英語版
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''.

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