Fitxa persona

Brief summary of my Curriculum Vitae. Licensed with Extraordinary Prize and First National Prize in Mathematical Sciences (1986). and Doctor with Extraordinary Award (1989) in Mathematical Sciences by the University of Valencia (UV). I am currently a university full professor of Algebra at the Facultat of Matemàtiques of the UV, a University where I provide services since 1986. I am leading a research team since 1993 whose research work has contributed significantly to the progress of the knowledge in Abstract Theory of Groups, Theory of Semigroups, Automata and Formal Languages and in the theory of Braces and the Yang-Baxter equation, answering open questions in these theories raised by reputed researchers and opening new lines of research. I have published 303 scientific articles in prestigious international journals of high impact. I contributed to the important and famous Wielandt program (1980) consisting in the analysis of the structure of a finite group by means of the study of subgroup embedding properties and characteristic classes of subgroups. We introduce normalisers and prefrattini subgroups in finite non-necessarily soluble groups: an intriguing challenge in Abstract Group Theory after the classification of finite simple groups. Our systematic study of maximal subgroups of finite groups turns out to be useful tool in asymptotic and probabilistic group theory. We also solved many open questions of the 'Kourovka Notebook: Unsolved Problems in Group Theory' that have contributed to create a theory of generalized subnormal subgroups which is crucial for a better understanding of the group structure. These contributions appear in the book 'Classes of Finite Groups', with Ezquerro, Springer, 2006 (759 citations in Google Scholar). I also contributed to develop a theory of totally and mutually permutable products of finite groups and their generalizations starting with the answer of a difficult question proposed by Maier. I opened a research line in the study of the classes of T-, PT- and PST-groups which are defined in terms of permutability of subgroups, and have written the package Permut to deal with permutability in finite groups for the computer algebra system GAP. The book 'Products of Finite Groups', with Esteban Romero and Asaad, W. De Gruyter, 2010 (501 citations in Google Scholar) presents the results published in this area until 2010. These books are basic references in Abstract Group Theory. More recently, I answered open questions on sigma-properties of finite groups from the 'Kourovka Notebook: Unsolved Problems in Group Theory', as well as questions on regular orbits with applications to Wolf's conjecture. In the context of the renowned generalised Rhodes' Type II conjectures, we proved an exhaustive description of the abelian kernel of an inverse semigroup showing an engaging and inspiring interplaying between Semigroups, Automata and profinite topologies. I have contributed to the solution of the problem of the classification of braces of order 64 and to the algebraic study of braces by means of Trifactorised Groups, Graph Theory and Representation Theory. Our team started to work in braces in 2019 with remarkable results and impact that led to my invitation to participate in prestigious workshops (Oberwolfach 2019, 2022, Będlewo, 2022), and the workshop at Banff International Research Station (Canada, 2024). The number of citations of my publications is, as of today, 5040 with an h-index equal to 31, taking Google Scholar as source. My research score is ResearchGate is 2275, which is higher than 96% of ResearchGate members and than 99% of researches with work related to Algebra. The impact of my research has enabled my inclusion in the prestigious ranking 'World's 2% Scientists' published by Stanford University. I have participated in Research Projects financed by Spanish National Public Organisations (15) and International Public Organisations (9) from 1988 to the present, since 2004 as principal investigator or coordinator of coordinated National Projects. I am collaborating with research groups based in Germany (2), Saudi Arabia (1), Australia (1), Austria (1), Belarus (1), Colombia (3), Egypt (2), United States (2) , France (2), Greece (1), Italy (1), Israel (1), Netherlands (1), Portugal (2), People's Republic of China (6), South African Republic (3), Ukraine (1), and 22 members of these research teams have made predoctoral and postdoctoral stays at the Universitat de València under my supervision. I have delivered talks in 46 International Meetings, of which 37 as main speaker. I have made 50 research visits to several foreign Universities. I am advisor of more than 86 scientific journals and of the Springer Nature publishing house, member of the editorial committee of 13 scientific journals. I am advisor of Spanish and Foreign Project Evaluation Agencies (Saudi Arabia, Colombia, European Science Foundation, Italy, Perú). I have been advisor of 14 doctoral theses and 9 Master's Thesis.

. Full Professor of Algebra.