Math
Abstract Algebra I
Train on Abstract Algebra I with 300 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
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See a problem from Abstract Algebra I before you begin.
Course topics
Course topics
Groups, subgroups, and generated structures
Cyclic and permutation groups
Homomorphisms, kernels, and normal subgroups
Quotient groups and direct products
Group actions, orbits, and stabilizers
Sylow theory and finite-group structure
Practice problems
Try a few Abstract Algebra I problems, each with a hint.
- Why subtraction is not a group law Free with an accountGroups, subgroups, and generated structures
- Normal forms in a dihedral generating set Free with an accountGroups, subgroups, and generated structures
- Images of cyclic groups are cyclic Cyclic and permutation groups
- Disjoint cycles commute Cyclic and permutation groups
- A cyclic homomorphism from one formula Homomorphisms, kernels, and normal subgroups
- A union of normal subgroups can fail Homomorphisms, kernels, and normal subgroups
- Kernels under a composite surjection Quotient groups and direct products
- Build a map into a direct product Quotient groups and direct products
- Symmetries acting on a square Group actions, orbits, and stabilizers
- The two Sylow counting constraints Sylow theory and finite-group structure