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Daniele Garzoni

Research interests:

My research is in group theory, and in the interplay between group theory and number theory.

I like asymptotic questions in finite group theory. For example, questions involving large finite simple groups, or permutation groups of large degree. I also like monodromy groups, and problems related to Hilbert's irreducibility theorem and specializations in number theory.

Here is my arXiv profile.


11. On the irreducibility of f(2^n, 3^m, X) and other such polynomials

      with Lior Bary-Soroker and Vlad Matei     arXiv

10. Probabilistic generation of finite almost simple groups

      with Jason Fulman and Robert Guralnick     arXiv


9. Conjugacy classes of derangements in finite groups of Lie type

    with Sean Eberhard     arXiv

    Trans. Amer. Math. Soc., to appear.

8. On the probability of generating invariably a finite simple group

    with Eilidh McKemmie     arXiv, journal

    J. Pure Appl. Algebra, 227(6) (2023), 107284.

7. Hilbert's irreducibility theorem via random walks

    with Lior Bary-Soroker     arXiv, journal

    Int. Math. Res. Not. 2023(14) (2023), 12512--12537.

6. Large minimal invariable generating sets in the finite symmetric groups

    with Nick Gill     arXiv, journal

    Israel J. Math. 255 (2023), 581--598.

5. On the number of conjugacy classes of a primitive permutation group

    with Nick Gill     arXiv, journal                                        

    Proc. Roy. Soc. Edinburgh Sect. A 153(1) (2023), 115-136.

4. Random generation with cycle type restrictions

    with Sean Eberhard     arXiv, journal

    Algebr. Comb. 4(1) (2021), 1-25.

3. Connected components in the invariably generating graph of a finite group

    Bull. Aust. Math. Soc. 104(3) (2021), 453-463.

    arXiv, journal

2. Minimal invariable generating sets

    with Andrea Lucchini     arXiv, journal

    J. Pure Appl. Algebra 224(1) (2020), 218-238.

1. The invariably generating graph of the alternating and symmetric groups

    J. Group Theory 23(6) (2020), 1081-1102.

    arXiv, journal

Not intended for publication:

    Probability of generation by random permutations of given cycle type

    with Sean Eberhard     arXiv 

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