3-local lower central series

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Definition

The 3-local lower central series of a group G is a descending series defined as follows. The i^{th} member, which we will denote as \gamma_i^{3-loc}(G) is defined as:

\gamma_i^{3-loc}(G) = \langle \gamma_i(H) \rangle where H varies over all subgroups of G that are generated by at most 3 elements and \gamma_i(H) denotes the i^{th} member of the lower central series of H.

G has 3-local nilpotency class (at most) c if and only if \gamma_{c + 1}^{3-loc}(G) is the trivial subgroup.

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