Papers

Coauthors:

Francesca Lisi (4), Sean Eberhard (3), Marco Barbieri (2), Andrea Lucchini (2), Pablo Spiga (2), Daniele Dona (1), Hongyi Huang (1), Elena Maini (1), Patricia Medina Capilla (1), Aluna Rizzoli (1), Mima Stanojkovski (1), Gareth Tracey (1)

On the left is the Foster graph (for its significance in my research, see Theorem 1.1 here).

All my preprints are available on arxiv or scholar . See also Researchgate.

Arithmetic properties of solubilizers

We give a direct short proof of the normalizer-solubilizer conjecture by Mousavi, Poozesh and Zamani.

arxiv (2026, 6pp)

Sylow synchronization in finite groups: the good case

with Hongyi Huang, Francesca Lisi and Aluna Rizzoli

We make progress on the Sylow synchronization conjecture, settling in particular the case of groups of odd order.

arxiv | data (2026, 11pp)

Cayley graphs of quasirandom groups

We build on recent work of Golsefidy-Srinivas, and conclude that expansion in a quasirandom group is always controlled by expansion in its simple quotients. Then, we extend some results for simple groups of bounded Lie rank to abstract quasirandom groups.

arxiv (2026, 20pp)

The base size of vertex-transitive cubic graphs

with Marco Barbieri and Pablo Spiga

We prove that, except for some small cases and a natural infinite family, all connected vertex-transitive cubic graphs have base size at most 2, i.e. fixing two vertices can break all symmetries. The proof relies on the Classification of Finite Simple Groups.

arxiv (2026, 37pp)

Diameter bounds for arbitrary finite groups and applications

with Sean Eberhard, Elena Maini and Gareth Tracey

We prove a polylog-type diameter bound for arbitrary finite groups, depending only on the nonabelian composition factors and the maximal exponent of a normal abelian section. There are several notable applications, including new diameter bounds for permutation groups and growth estimates for a broad class of residually finite groups.

arxiv (2026, 35pp)

Expanding groups with large diameter

with Sean Eberhard

We exhibit a sequence of finite groups admitting very different Cayley graphs, namely expanders and with super-polylogarithmic diameter. This answers a question by Pyber and Szabó from 2013.

arxiv (2026, 8pp)

15. On the maximal subgroups of almost simple and primitive perfect groups, Math. Proc. Cambridge Philos. Soc. (2026)

with Patricia Medina Capilla

We prove that every maximal subgroup of every finite almost simple group is nearly perfect, in the sense that the 10th term of its derived series is always perfect. In fact we obtain the same result for primitive perfect groups.

arxiv | journal (2026, 17pp)

Groups that produce expander graphs

A survey on groups whose Cayley/Schreier graphs are good candidate to be expanders. There are minor new results and a few questions.

arxiv (2025, 11pp)

Exponent and number of generators in a finite group

We observe that the number of generatos of a finite group can be bounded by the ratio between the order and the exponent.

arxiv (2025, 3pp)

14. Sylow subgroups for distinct primes and intersection of nilpotent subgroups, J. Algebra (2026)

with Francesca Lisi

We propose a general conjecture about synchronized intersections of Sylow subgroups, which unifies previous lines of investigation and results on the intersection of nilpotent subgroups in finite groups.

arxiv | journal (14pp)

13. On stabilizers in finite permutation groups, Bull. London Math. Soc. (2026)

We prove several results concerning breaking-symmetry partitions in finite permutation groups. We answer a few questions of Babai.

arxiv | journal (15pp)

12. Quasirandom and quasisimple groups, Discrete Anal. (2025)

with Marco Barbieri

We give a group theoretical description of the finite groups having all nontrivial irreducible representations of large degree.

arxiv | journal (24pp)

11. Probabilistic construction of some extremal p-groups, J. Algebra (2025)

with Sean Eberhard

We use random bilinear maps to construct finite p-groups of class 2 with unexpected properties, answering a few questions in the literature.

arxiv | journal (18pp)

10. The diameter of random Schreier graphs, European J. Combin. (2025)

with Daniele Dona

We show that Schreier graphs on sufficiently many random elements have optimal diameter with high probability.

arxiv | journal (8pp)

9. Fixing two points in primitive solvable groups, Commun. Algebra (2025)

with Francesca Lisi

We prove that in a primitive group of odd order there are always two points whose pointwise stabilizer is abelian.

arxiv | journal (6pp)

8. On finite d-maximal groups, Bull. London Math. Soc. (2024)

with Andrea Lucchini and Mima Stanojkovski

We start a long overdue investigation of the finite groups that require more generators than every proper subgroup.

arxiv | journal (17pp)

7. Products of subgroups, subnormality, and relative orders of elements, Ars Math. Contemp. (2024)

We remark connections between two apparently unrelated phenomena: when the cardinality of the product of two subgroups divides the order of the group, and when the power of an element lies in a subgroup. The connecting notion is subnormality.

arxiv | journal (9pp)

6. On groups with large verbal quotients, J. Group Theory (2024)

with Francesca Lisi

We study w-maximal and weakly w-maximal groups, as well as their applications.

arxiv | journal (15pp)

5. The growth of abelian sections, Ann. Mat. Pura Appl. (2023)

We introduce a function that measures the cardinality of the abelian quotients of the subgroups at a given index, in analogy with the subgroup growth and the representation growth.

arxiv | journal (20pp)

4. Nilpotent subgroups of class 2 in finite groups, Proc. Amer. Math. Soc. (2022)

We prove that every large finite group contains a large nilpotent subgroup of class at most 2, answering a question of Pyber from 1997. In fact this paper implicitly introduces ab-maximal groups, observes that they have class at most 2 and shows that every large finite group contains a large ab-maximal subgroup.

arxiv | journal (4pp)

3. Random Schreier graphs and expanders, J. Algebraic Combin. (2022)

We show that Schreier graphs on sufficiently many random elements are expanders with high probability. This generalizes a famous theorem of Alon and Roichman.

arxiv | journal (13pp)

2. Abelian sections of the symmetric groups with respect to their index, Arch. Math. (Basel) (2022)

We prove that large subgroups of the symmetric group have very small abelianization, in particular the smallest possible with respect to the index.

arxiv | journal (10pp)

On finite groups with polynomial diameter

We make an observation concerning a deep theorem of Breuillard and Tointon.

arxiv (2021, 4pp)

1. A subexponential bound on the cardinality of abelian quotients in finite transitive groups, Bull. London Math. Soc. (2021)

with Andrea Lucchini and Pablo Spiga

We prove that transitive permutation groups have small abelianization, answering a question of Kovács and Praeger from 1989.

arxix | journal (6pp)

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