Symbolic computation with infinite sequences of p-groups with fixed coclass

Dörte Feichtenschlager

ISBN 978-3-8325-2588-0
144 pages, year of publication: 2010
price: 34.50 €
Symbolic computation with infinite sequences of p-groups with fixed coclass

The classification of finite p-groups is a much investigated problem, though in general it seems impossible. Leedham-Green & Newman defined a new invariant for finite p-groups, the coclass. They suggested to try to classify finite p-groups by coclass. One step towards such a classification was the introduction of so-called infinite coclass sequences by du Sautoy and Eick & Leedham-Green. The groups in such a sequence can be described by a parametrised presentation. For prime 2 and a fixed coclass r it holds that almost all 2-groups of coclass r fall into finitely many infinite coclass sequences. So describing the infinite sequences yields an almost classification in these cases. In this work it is shown that using the parametrised presentations one can compute certain invariants for almost all groups in an infinite coclass sequence, especially the Schur multiplicator. This is done by introducing a way to work with almost all groups at a time by a symbolic computation.