MATH 323 Algebra I

Symmetries of regular polygons and polyhedra. Permutation groups and abstract groups. Lagrange's Theorem and the Orbit-Stabilizer Theorem. Quotient groups and the Isomorphism Theorems. Sylow's Theorem. Direct and Semidirect Product Recognition Theorems. Symmetric and alternating groups. The simplicity of the alternating groups of degree at least 5. Classical linear groups. Rings. The Chinese Remainder Theorem, primitive roots, and the Structure Theorem for Finitely-Generated Abelian Groups. Jordan-Holder Theorem. Credit units: 3 ECTS Credit units: 6.

Autumn Semester (Matthew Gelvin)

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