Author(s)

Daniel C. Mayer

Naglergasse 53, Graz, Austria.

Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their automorphism groups under these isomorphisms is described with simple transformation laws. For the tree of finite 3-groups with elementary bicyclic commutator qu-otient, the information content of each coclass subtree with metabelian main-line is shown to be finite. As a striking novelty in this paper, evidence is provided of co-periodicity isomorphisms between coclass forests which reduce the information content of the entire metabelian skeleton and a significant part of non-metabelian vertices to a finite amount of data.

Finite p-Groups, Descendant Trees, Pro-p Groups, Coclass Forests, Generator Rank, Relation Rank, Nuclear Rank, Parametrized Polycyclic Pc-Presentations, Automorphism Groups, Central Series, Two-Step Centralizers, Commutator Calculus, Transfer Kernels, Abelian Quotient Invariants, p-Group Generation Algorithm

Mayer, D. (2018) Co-Periodicity Isomorphisms between Forests of Finite p-Groups. Advances in Pure Mathematics, 8, 77-140. doi: 10.4236/apm.2018.81006.