Papers

Coauthors:

Sean Eberhard (3), Francesca Lisi (3), Marco Barbieri (2), Andrea Lucchini (2), Pablo Spiga (2), Daniele Dona (1), Elena Maini (1), Patricia Medina Capilla (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 .

Cayley graphs of quasirandom groups

We extend recent work of Golsefidy-Srinivas, concluding 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.

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, which essentially was an untouched problem. There are several notable applications.

arxiv (2026, 35pp)

Expanding groups with large diameter

with Sean Eberhard

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

arxiv (2026, 8pp)

On the maximal subgroups of almost simple and primitive perfect groups

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 (2026, 14pp)

Groups that produce expander graphs

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

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 only 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 link some apparently unrelated phenomena in finite group theory.

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 and study a function the measures the abelian sections of the subgroups at a given index in an abstract group, on the footsteps of other well known functions such as subgroup and reprsesentation growths.

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. This answers a question of Pyber from 1997.

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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