TITLE:
Co-Periodicity Isomorphisms between Forests of Finite p-Groups
AUTHORS:
Daniel C. Mayer
KEYWORDS:
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
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.1,
January
31,
2018
ABSTRACT: 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.