{
  "id": "2205.06173",
  "version": "v1",
  "published": "2022-05-12T16:02:16.000Z",
  "updated": "2022-05-12T16:02:16.000Z",
  "title": "Actions of $\\operatorname{Alt}(n)$ on groups of finite Morley rank without involutions",
  "authors": [
    "Tuna Altınel",
    "Joshua Wiscons"
  ],
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "We investigate faithful representations of $\\operatorname{Alt}(n)$ as automorphisms of a connected group $G$ of finite Morley rank. We target a lower bound of $n$ on the rank of such a nonsolvable $G$, and our main result achieves this in the case when $G$ is without involutions. In the course of our analysis, we also prove a corresponding bound for solvable $G$ by leveraging recent results on the abelian case. We conclude with an application towards establishing natural limits to the degree of generic transitivity for permutation groups of finite Morley rank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-12T16:02:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "20F11",
      "20C30"
    ],
    "keywords": [
      "finite morley rank",
      "involutions",
      "main result achieves",
      "establishing natural limits",
      "abelian case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}