Algebra Seminar

An infinite pro-p-group allows simultaneous analysis of certain properties of infinitely many finite p-groups. In a similar way to complex Lie groups, p-adic analytic pro-p-groups are associated to Lie algebras via exp-log. Also the Cayley map provides a tool to connect the groups with Lie algebras. This map gives a correspondence between the lower central series of the group and the lower central series of the Lie order. The advantage of this technique is that it extends also to linear pro-p-groups over GF(p)[[t]].

Lie algebras can also be used to recognize the corresponding groups.