{
  "id": "2009.01044",
  "version": "v1",
  "published": "2020-09-01T16:59:45.000Z",
  "updated": "2020-09-01T16:59:45.000Z",
  "title": "The order of the product of two elements in periodic groups",
  "authors": [
    "M. Amiri",
    "I. Lima"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "An old problem in group theory is that of describing how the order of an element behaves under multiplication. Let $G$ be a periodic group, and let $LCM(G)$ be the set of all $x\\in G$ such that $o(x)$ is less than $exp(G)$ and $o(xz)$ divides the least common multiple of $o(x)$ and $o(z)$ for all $z$ in $G$. In this article, we prove that the subgroup generated by $LCM(G)$ is a nilpotent characteristic subgroup of $G$ whenever $G$ is a solvable group or $G$ is a finite group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-01T16:59:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic group",
      "nilpotent characteristic subgroup",
      "group theory",
      "old problem",
      "element behaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}