{
  "id": "1403.1425",
  "version": "v2",
  "published": "2014-03-06T12:03:12.000Z",
  "updated": "2014-09-12T09:32:07.000Z",
  "title": "Cohomology of finite groups without homological algebra",
  "authors": [
    "Sergei O. Ivanov",
    "Nikolay N. Mostovsky"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove explicit and elementary formulas for the group homology and cohomology of a finite group with coefficients in any module. We describe in elementary terms the cohomology algebra $H^*(G,k)$ as a graded algebra for a finite group $G$ and a commutative ring $k.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-06T12:03:12.000Z",
      "abstract": "This note is devoted to a proof of explicit formulas for the homology and cohomology of a finite group that uses only simple operations such as quotient, tensor product and G-invariants. These formulas are interesting because they do not use the notion of a complex. In other words, they do not use homological algebra at all. At the end of the note we prove a few well-known statements in order to show how these formulas can be used.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-12T09:32:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "homological algebra",
      "cohomology algebra",
      "elementary terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.1425I"
    }
  }
}