%0 Journal Article
%T Co-Periodicity Isomorphisms between Forests of Finite <I>p</I>-Groups
%A Daniel C. Mayer
%J Advances in Pure Mathematics
%P 77-140
%@ 2160-0384
%D 2018
%I Scientific Research Publishing
%R 10.4236/apm.2018.81006
%X Based on a general theory of descendant trees of finite <em abs_visibility=\"true\">p</em>-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.
%K Finite &lt
%K i&gt
%K p&lt
%K /i&gt
%K -Groups
%K Descendant Trees
%K Pro-&lt
%K i&gt
%K p&lt
%K /I&gt
%K Groups
%K Coclass Forests
%K Generator Rank
%K Relation Rank
%K Nuclear Rank
%K Parametrized Polycyclic Pc-Presentations
%K Automorphism Groups
%K Central Series
%K Two-Step  Centralizers
%K Commutator Calculus
%K Transfer Kernels
%K Abelian Quotient  Invariants
%K &lt
%K i&gt
%K p&lt
%K /i&gt
%K -Group Generation Algorithm
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=82163