in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

A class of Preparata-like group codes is considered. It was suggested by Baker, van Lint and Wilson and re-stated in a different form by Ericson. We show that all such codes are inside the Hamming code providing its partition into the cosets of the Preparata-like codes. This partition induces 2-resolvable Steiner quadruple systems.

It is proved in this paper that for m ≡ 0; 2; 6; 10 (mod 12) there exists a resolvable group divisible design of order v, block size 4 and group size m if and only v ≡ 0 (mod 4), v ≡ 0 (modm), v − m ≡ 0 (mod 3), except when (3; 12) and except possibly when (3; 264); (3; 372); (8; 80); (8; 104), (9; 396) (40; 400) or (40; 520). c © 2002 Elsevier Science B.V. All rights reserved.

Let G be a finite p-superperfect group. A conjecture of F. Cohen suggests that ΩBGp is resolvable by finitely many fibrations over spheres and iterated loop spaces on spheres, where (−)p denotes the p-completion functor of Bousfield and Kan. We produce a counter-example to this conjecture and discuss some related aspects of the homotopy type of ΩBGp .