Basic group theory and first aspects of groups of permutations
Products: cartesian, semidirect, wreath, direct and inverse limits
Generation of groups; free groups , varieties, presentations,, Cayley’s graphs, growth.
Groups acting on rooted trees.
Basic theory of nilpotent groups
Knowledge acquired: Basic ideas and techniques in abstract group theory, with emphasis on some aspects of infinite groups for which reseach is currently very active.
Competence acquired: that corcening some parts of the theory of abstract groups that may have fruitful intersections with other areas of mathematics.
Skills acquired (at the end of the course): read a modern research article about abstract groups,, being able to fill those parts usually left to the reader.
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 225
Hours reserved to private study and other indivual formative activities: 153
Hours for lectures: 72
Basic group theor and first aspects of groups of permutations
Products: cartesian, semidirect, wreath, direct and inverse limits
Generation of groups; free groups , varieties, presentations,, Cayley’s graphs, growth.
Groups acting on rooted trees.
Basic theory of nilpotent groups