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  • A characterization of $$A_{...
    A characterization of $$A_{5}$$ A 5 by its Same-order type
    Taghvasani, L. Jafari; Zarrin, M.

    Monatshefte für Mathematik, 3/2017, Letnik: 182, Številka: 3
    Journal Article

    Let G be a group. The same-order type of G may be defined to be the set of sizes of equivalence classes for the equivalence relation ∼ on G defined by ∀ g , h ∈ G g ∼ h ⟺ | g | = | h | . Shen et al. (Monatsh Math 160:337–341,2010), showed that A 5 is the only group with the same-order type { 1 , 15 , 20 , 24 } . In this paper, among other things, we prove that a nonabelian simple group G has same-order type with just four members if and only if G ≅ A 5 .

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