A natural problem in group theory is: what can we say about a group in which all subgroups of a relevant family of subgroups satisfy a certain property? We intend to make contributions along these lines.
When a factor group G=AB is considered as a product of two subgroups, related with certain permutability conditions, the natural question is to determine what we can say about G from the properties of A and B, and what we can say about A and B from properties of G.
The fathoms are associated to trifactor groups with structural properties that effectively determine solutions of the quantum Yang-Baxter equation.
Group Theory and its representations.
Certain classes of groups are defined by the actions of the groups with regard to the main factors or other normal sections. Special importance is attached to subgroups that cover or avoid all the main factors of the group, as well as actions that determine flanges of special type.
Recognition and machine learning techniques applied to linear and nonlinear models. Continuous Distance Learning. Heterogeneous and multi-dimensional data mining, with special emphasis on image analysis and recovery and the processing of audio and video signals.
In the field of computer science, there has been a growing interest in the study of semigroups and monoids in relation to automata and formal languages. We aim to apply techniques from group theory and universal algebra to the analysis of these objects.
In recent years, groups where all subnormal subgroups are normal, permutable, or Sylow-permutable have been of interest, both in terms of finite groups and extensions to classes of infinite groups. We have also developed computational techniques to study these groups with GAP.
