Groups are a fundamental concept in abstract algebra. Understanding their definitions and properties and studying examples is important in order to gain a comprehensive understanding of algebraic structures.
- Define and understand the basic concepts of groups and properties.
- Define and distinguish between various types of groups, such as finite and infinite groups, abelian and non-abelian groups, and cyclic and non-cyclic groups..
- Determine whether a given subset of a group is a subgroup.
- Prove basic results involving various types of groups.
- Solve basic problems involving various groups and its subgroups.