Algebra: Practice Exam Solutions

Related lectures (31)

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Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Delves into the symmetries of regular polygons, including the dihedral group and left cosets in a finite group.

Explores the philosophy of understanding a group through its subgroups' structure, focusing on finite groups.

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

Covers Cauchy's theorem, classification of finite abelian groups, direct product properties, and more.