We give a complete answer to the GFR conjecture, proposed by Conder, Doyle, Tucker and Watkins: “All but finitely many Frobenius groups F=N⋊H with a given complement H have a GFR, with the exception when |H| is odd and N is Abelian but not an elementary 2-group”. Actually, we prove something stronger, we enumerate asymptotically GFRs; we show that, besides the exceptions listed above, as |N| tends to infinity, the proportion of GFRs among all Cayley graphs over N containing F in their automorphism group tends to 1.
Spiga, P. (2020). On the existence of graphical Frobenius representations and their asymptotic enumeration. JOURNAL OF COMBINATORIAL THEORY, 142(May 2020), 210-243 [10.1016/j.jctb.2019.10.003].
On the existence of graphical Frobenius representations and their asymptotic enumeration
Spiga P.
2020
Abstract
We give a complete answer to the GFR conjecture, proposed by Conder, Doyle, Tucker and Watkins: “All but finitely many Frobenius groups F=N⋊H with a given complement H have a GFR, with the exception when |H| is odd and N is Abelian but not an elementary 2-group”. Actually, we prove something stronger, we enumerate asymptotically GFRs; we show that, besides the exceptions listed above, as |N| tends to infinity, the proportion of GFRs among all Cayley graphs over N containing F in their automorphism group tends to 1.File | Dimensione | Formato | |
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