Geodesic
On Peiffer central series
Glasgow mathematical journal, Tome 40 (1998) no. 2, pp. 177-185

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a group. A precrossed G-module is a group homomorphism ∂: M → G together with a group action (g, m) ↦gm of G on M, such that ∂(gm) = g(∂m)g−1. The Peiffer commutator < m, m′ > of two elements m, m′ ∊ M is denned as< m, m′ >= mm′ m−1(∂mm′)−1If all Peiffer commutators are trivial, the precrossed G-module is said to be a crossed G-module. The subgroup < M, M > generated by all Peiffer commutators is called the Peiffer subgroup of M; it is the second term of a lower Peiffer central series (see below). The following table indicates how these concepts reduce to more standard concepts when restrictions are placed on ∂ and G. 
Ellis, Graham. On Peiffer central series. Glasgow mathematical journal, Tome 40 (1998) no. 2, pp. 177-185. doi: 10.1017/S0017089500032493
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