Conchita Martínez-Pérez

Cohomological finiteness conditions for elementary amenable groups

Abstract It is proved that every elementary amenable group of type FP∞ admits a cocompact classifying space for proper actions.

A spectral sequence in Bredon (co)homology

Abstract We construct a spectral sequence which relates the Bredon (co)homology groups of a group G with respect to two different families of subgroups of G satisfying certain restrictions. This allow us to obtain bounds for the (co)homological dimensions of G and to construct a Lyndon–Hochschild–Serre spectral sequence in Bredon (co)homology.

Is the class of cyclic codes asymptotically good

There is the long-standing question whether the class of cyclic codes is asymptotically good. By an old result of Lin and Weldon, long Bose-Chaudhuri-Hocquenhem (BCH) codes are asymptotically bad. Berman proved that cyclic codes are asymptotically bad if only finitely many primes are involved in the lengths of the codes. We investigate further classes of cyclic codes which also turn out to be asymptotically bad. Based on reduction arguments we give some evidence that there are asymptotically good sequences of binary cyclic codes in which all lengths are prime numbers provided there is any asymptotically good sequence of binary cyclic codes.

Self-dual codes and modules for finite groups in characteristic two

Using representation theoretical methods we investigate self-dual group codes and their extensions in characteristic 2. We prove that the existence of a self-dual extended group code heavily depends on a particular structure of the group algebra KG which can be checked by an easy-to-handle criteria in elementary number theory. Surprisingly, in the binary case such a code is doubly even if the converse of Gleasons theorem holds true, i.e., the length of the code is divisible by 8. Furthermore, we give a short representation theoretical proof of an earlier result of Sloane and Thompson which states that a binary self-dual group code is never doubly even if the Sylow 2-subgroups of G are cyclic. It turns out that exactly in the case of a cyclic or Klein four group as Sylow 2-subgroup doubly even group codes do not exist.

The proper geometric dimension of the mapping class group

We show that the mapping class group of a closed surface admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension.

COHOMOLOGICAL FINITENESS PROPERTIES OF THE BRIN-THOMPSON-HIGMAN GROUPS 2V AND 3V

We show that Brins generalisations 2V and 3V of the Thompson-Higman group V are of type FP1. Our methods also give a new proof that both groups are nitely presented.

BREDON COHOMOLOGICAL FINITENESS CONDITIONS FOR GENERALISATIONS OF THOMPSON GROUPS

We define a family of groups that generalises Thompsons groups

Self-Dual Doubly Even

T

2

and

-Quasi-Cyclic Transitive Codes Are Asymptotically Good

G