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.
Quotients of subdirect products of groups.
Relative commutator associated with varieties of -nilpotent and of -solvable groups
In this note we determine explicit formulas for the relative commutator of groups with respect to the subvarieties of -nilpotent groups and of -solvable groups. In particular these formulas give a characterization of the extensions of groups that are central relatively to these subvarieties.
Remarks on Characters of Discrete Nilpotent Groups.
Representations of Certain Verbal Wreath Products by Matrices.
Restoration of structure
Seminilpotent groups
Soluble products of nilpotent groups
Some remarks on almost finitely generated nilpotent groups.
We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if Gp is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that Gp ≅ Hp for all p. The we have proper set-inclusions:{fg} ⊂ {fg-like} ⊂ {fgp}.We examine the extent to which fg-like nilpotent groups satisfy the axioms for a Serre class. We obtain a complete answer only in the case that [G, G] is finite. (The collection of fgp nilpotent groups...
Subcubic growth of the averaged Dehn function for a class 2 nilpotent group.
Subgroups of finite index in nilpotent groups.
Supplemented nilpotent groups
Symmetric words in nilpotent groups of class ≤ 3
Systèmes sous-elliptiques
The Finiteness Obstructions for Nilpotent Spaces lie in D (...).
The nilpotency of some groups with all subgroups subnormal.
Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or min- G. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.