A natural line of research in the field of group theory is the study of the arithmetic and structural properties of groups, in which he has consolidated experience of more than fifteen years. The techniques of group class theory and their representations are fundamental to this study. These techniques can also be used to study structural problems of semigroups, based on the already existing study of the interactions between groups and automata and formal languages, as well as the interactions between three-factored groups, group actions, fathoms, and the Yang-Baxter equation. This group aims to advance our understanding of:
(I) Factored groups. Structural study of fathoms and their relationship to the Yang-Baxter equation.
(II) Actions of groups on certain normal subgroups and their principal factors.
(III) Structural influence of the relationships between various families of subgroups and their immersion properties.
(IV) The normal and permutable structure of certain families of groups with finiteness conditions.
(V) The role of groups in semigroups and their representations. Formal languages and automata.
This group works in coordination with other teams based at the University of Zaragoza and the Public University of Navarra, on the one hand, and at the Polytechnic University of Valencia, on the other.
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