Profinite Groups and Cohomology

In mathematics, a group is a set (an accumulation of items) together with a certain operation. For example: the integers with addition, the symmetries of an equilateral triangle. Being one of the simplest algebraic structures, groups are ubiquitous in mathematics and have applications in other disciplines. Informally, a group is called profinite if it can be assembled from finite groups in a certain manner. The above symmetries are a finite group: there are only three reflections along the axes and the rotations around 120, 240 and 360 degrees. On the other hand, cohomology is an algebraic tool that can discern different geometric objects by looking at their “holes”. For example, one can discern a ball from a donut using it. There is a counterpart for groups, so group cohomology is a tool that can discern different groups. This project forms a part in answering a question about group cohomology of profinite groups.

Faculty Supervisor:

Alejandro Adem

Student:

Partner:

University of Southampton

Discipline:

Mathematics

Sector:

Education

University:

The University of British Columbia

Program: