{
  "id": "1401.2017",
  "version": "v1",
  "published": "2014-01-09T14:32:10.000Z",
  "updated": "2014-01-09T14:32:10.000Z",
  "title": "Moufang sets of finite Morley rank of odd type",
  "authors": [
    "Joshua Wiscons"
  ],
  "doi": "10.1016/j.jalgebra.2014.01.001",
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "We show that for a wide class of groups of finite Morley rank the presence of a split $BN$-pair of Tits rank $1$ forces the group to be of the form $\\operatorname{PSL}_2$ and the $BN$-pair to be standard. Our approach is via the theory of Moufang sets. Specifically, we investigate infinite and so-called hereditarily proper Moufang sets of finite Morley rank in the case where the little projective group has no infinite elementary abelian $2$-subgroups and show that all such Moufang sets are standard (and thus associated to $\\operatorname{PSL}_2(F)$ for $F$ an algebraically closed field of characteristic not $2$) provided the Hua subgroups are nilpotent. Further, we prove that the same conclusion can be reached whenever the Hua subgroups are $L$-groups and the root groups are not simple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-09T14:32:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E42",
      "03C60"
    ],
    "keywords": [
      "finite morley rank",
      "odd type",
      "hua subgroups",
      "hereditarily proper moufang sets",
      "infinite elementary abelian"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2017W"
    }
  }
}