Partially defined cocycles and the Maslov index for a local ring
In this paper we study some aspects of the cohomology of groups and we construct a central extension of the symplectic group .
P-equivalence de groupes nilpotents.
Permutation modules and projective resolutions.
Perturbations of centre-fixing dynamical systems.
Phantom maps and purity in modular representation theory, I
Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms we need...
Plane Motion Groups and Virtual Poincaré Duality of Dimension Two.
p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.
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...
Poincaré Duality and Groups of Type (FP).
Poincaré duality groups of dimension two.
Poincaré duality groups of dimension two, II.
Polynomial Maps on Groups. II.
Presentations of finite simple groups: a computational approach
All finite simple groups of Lie type of rank over a field of size , with the possible exception of the Ree groups , have presentations with at most 49 relations and bit-length . Moreover, and have presentations with 3 generators; 7 relations and bit-length , while has a presentation with 6 generators, 25 relations and bit-length .
Protomodularity, descent, and semidirect products.