-adic completions and automorphisms of nilpotent groups
P-equivalence de groupes nilpotents.
P-nilpotent completion is not idempotent.
Let P be an arbitrary set of primes. The P-nilpotent completion of a group G is defined by the group homomorphism η: G → GP' where GP' = inv lim(G/ΓiG)P. Here Γ2G is the commutator subgroup [G,G] and ΓiG the subgroup [G, Γi−1G] when i > 2. In this paper, we prove that P-nilpotent completion of an infinitely generated free group F does not induce an isomorphism on the first homology group with ZP coefficients. Hence, P-nilpotent completion is not idempotent. Another important consequence of...
Polycyclic groups, Lie algebras and algebraic groups.
Positively ramified extensions of algebraic number fields.
Projections in C*-Algebras of nilpotent groups.