{
  "id": "2009.05627",
  "version": "v1",
  "published": "2020-09-11T19:21:01.000Z",
  "updated": "2020-09-11T19:21:01.000Z",
  "title": "Block-groups and Hall relations",
  "authors": [
    "Azza M. Gaysin",
    "Mikhail V. Volkov"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "A binary relation on a finite set is called a Hall relation if it contains a permutation of the set. Under the usual relational product, Hall relations form a semigroup which is known to be a block-group, that is, a semigroup with at most one idempotent in each $\\mathrsfs{R}$-class and each $\\mathrsfs{L}$-class. Here we show that in a certain sense, the converse is true: every block-group divides a semigroup of Hall relations on a finite set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-11T19:21:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M20",
      "20M30"
    ],
    "keywords": [
      "finite set",
      "usual relational product",
      "hall relations form",
      "binary relation",
      "block-group divides"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}