MATA221 Algebra 1: Groups (5 cr)

Basics of abstract algebra: binary operations and homomorphisms, groups

After completing the course successfully the student

• is familiar with the concepts of a set equipped with an operation and homomorphism and is able to examine their properties even in an abstract setting
• knows how to find out, whether a set equipped with an operation is a group.
• is able to determine whether a subset of a group is a subgroup, and if the the subgroup is a normal subgroup
• knows how to compute with permutations
• is familiar with the concept of a factor group and especially, knows how to compute with congruence classes
• is able to examine the structure of a group, using for example Lagrange's theorem

Linear algebra and geometry 1, basics of modular arithmetics (for instance from the course Algebra 1: Rings and Fields)

Lecture notes (in Finnish)

The contents of the study-module correspond to: T.W. Hungerford, Abstract Algebra: an introduction, chapter 7.