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Co-Periodicity Isomorphisms between Forests of Finite <I>p</I>-Groups
Naglergasse 53, Graz, Austria
- 1 Naglergasse 53, Graz, Austria
Advances in Pure Mathematics·Volume 08 (2018)·Pages 77–140·Published 9 January 2018·DOI10.4236/apm.2018.81006
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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.
KeywordsFinite <i>p</i>-GroupsDescendant TreesPro-<i>p</I>GroupsCoclass ForestsGenerator RankRelation RankNuclear RankParametrized Polycyclic Pc-PresentationsAutomorphism GroupsCentral SeriesTwo-Step Centralizers
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