Group Theory and Applications (n. 2022PSTWLB)
Type
PRIN 2022, D.D. n. 104 del 2 febbraio 2022
CUP
C53D23002520006
Principal Investigator
Eugenio Giannelli (Università degli Studi di Firenze)
Other research units
UO1 - Eugenio GIANNELLI - Università degli Studi di FIRENZE
UO2 - Pablo SPIGA - Università degli Studi MILANO-BICOCCA
UO3 - Andrea LUCCHINI - Università degli Studi di PADOVA
UO4 - Marco TROMBETTI - Università degli Studi di Napoli Federico II
UO5 - Mercede MAJ - Università degli Studi di SALERNO
Duration
28/09/2023 - 30/09/2025
Description
One of our purpose the investigation of generating properties of groups with algebraic and combinatorial methods, aiming at solving some of the several open problems in this rich line of research. Leaving the realm of finite groups, we intend to focus our attention on the study of words and Verbal Subgroups in (profinite) groups. This active field of research has been at the center of the interest of the mathematical community since 1957 when, in his famous Edmonton Notes, Hall proposed several important questions on group words. Some of these do not admit affirmative solutions in general, but they all answer positively when restricted to the case of infinite linear groups. Motivated by this result of Merzljakov, we will focus our attention on the study of this important class of groups. Moreover, the study of group-words proved to have several important applications, like for instance the positive solution given by Nikolov and Segal to a famous question of Serre. Our goal is to advance in the study of word properties, most notably conciseness, as well as in the investigation of
Engel-words and Engel-elements in groups.
Activities
Conferenza: Topics in group theory, https://events.math.unipd.it/tgt/
Assegno di ricerca, assegnato a Daniele Nemmi
Related publications
1) Anzanello, Jessica; Lucchini, Andrea; Tracey, Gareth The Chebotarev invariant for direct products of nonabelian finite simple groups. Proc. Amer. Math. Soc. 153 (2025), no. 7, 2847–2861.
2) Costantini, Mauro; Lucchini, Andrea; Nemmi, Daniele Abelian supplements in almost simple groups. Forum Math. Sigma 13 (2025), Paper No. e14, 33 pp.
3) Lucchini, Andrea; Sabatini, Luca; Stanojkovski, Mima On finite d-maximal groups. Bull. Lond. Math. Soc. 56 (2024), no. 3, 1054–1070.
4) Lucchini, Andrea Solubilizers in profinite groups. J. Algebra 647 (2024), 619–632.
5) Lucchini, Andrea; Nemmi, Daniele On the connectivity of the generating and rank graphs of finite groups. J. Algebra 665 (2025), 131–144.
6) Detomi, Eloisa; Morigi, Marta; Shumyatsky, Pavel On groups with BFC-covered word values. J. Algebra 659 (2024), 132–147.
7) Detomi, Eloisa; Morigi, Marta; Shumyatsky, Pavel; Groups with a covering condition on commutators. Internat. J. Algebra Comput. 35 (2025), no. 5, 759–770.
8) E. Detomi, A. Lucchini, M. Morigi, P. Shumyatsky, Probabilistic properties of profinite groups. Israel J. Math., To appear, 10.1007/s11856-025-2807-1, arXiv:2304.04573.
