Geodesic
Generation of the lower central series II
Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 193-201

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In this article, we obtain results on commutators in Sylow subgroups of the lower central series, extending the work of Dark and Newell [2], Rodney [12, 13] and Aschbacher and the author [1, 6, 7].Some notation is required for the statement of the main results. Let r be a positive integer and defineandwhere x1, ..., xr, are elements in a group G. Let ΓrG = {[x1, ..., xr]∣ x1 ∈ G} be the set of r-fold commutators in G. Then Lr,G = 〈ΓrG〉 is the rth term in the lower central series of G. Set L∞G = ∩ Lr,G. 
Guralnick, Robert M. Generation of the lower central series II. Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 193-201. doi: 10.1017/S0017089500005619
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