{
  "id": "math/0601589",
  "version": "v2",
  "published": "2006-01-24T18:40:55.000Z",
  "updated": "2006-07-31T15:54:50.000Z",
  "title": "Large groups and their periodic quotients",
  "authors": [
    "A. Yu. Olshanskii",
    "D. V. Osin"
  ],
  "comment": "A section about periodic groups is added",
  "categories": [
    "math.GR"
  ],
  "abstract": "We first give a short group theoretic proof of the following result of Lackenby. If $G$ is a large group, $H$ is a finite index subgroup of $G$ admitting an epimorphism onto a non--cyclic free group, and $g$ is an element of $H$, then the quotient of $G$ by the normal subgroup generated by $g^n$ is large for all but finitely many $n\\in \\mathbb Z$. In the second part of this note we use similar methods to show that for every infinite sequence of primes $(p_1, p_2, ...)$, there exists an infinite finitely generated periodic group $Q$ with descending normal series $Q=Q_0\\rhd Q_1\\rhd ... $, such that $\\bigcap_i Q_i=\\{1\\} $ and $Q_{i-1}/Q_i$ is either trivial or abelian of exponent $p_i$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-07-31T15:54:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "large group",
      "periodic quotients",
      "short group theoretic proof",
      "finite index subgroup",
      "infinite finitely generated periodic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1589O"
    }
  }
}