{
  "id": "1802.03344",
  "version": "v1",
  "published": "2018-02-09T16:50:28.000Z",
  "updated": "2018-02-09T16:50:28.000Z",
  "title": "Co-periodicity isomorphisms between forests of finite p-groups",
  "authors": [
    "Daniel C. Mayer"
  ],
  "comment": "49 pages, 17 figures, 11 tables",
  "journal": "Adv. Pure Math. 8 (2018), no. 1, 77--140",
  "doi": "10.4236/apm.2018.81006",
  "categories": [
    "math.GR"
  ],
  "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 quotient, the information content of each coclass subtree with metabelian mainline 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-09T16:50:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C63",
      "20D15",
      "20E18",
      "20E22",
      "20F05",
      "20F12",
      "20F14"
    ],
    "keywords": [
      "finite p-groups",
      "co-periodicity isomorphisms",
      "coclass subtree",
      "information content",
      "elementary bicyclic commutator quotient"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}