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Includes: Statement and proof of Primary Decomposition Theorem Primary decomposition theorem from associated prime. It uses minimal polynomial of a matrix to write a vector space as a direct sum of invariant subspaces.

Includes: statement and proof of Orbit-Stabilizer Theorem. Orbit-Stabilizer Theorem is a combinatorial result in group theory. This theorem is often used in conjunction with Lagrange's theorem.

Provides information about: 1. Definition of commutator of a group G 2. Proof of the theorem Derived group of a group is a normal subgroup. 3. G/G' is abelian. 4. Other related theorem

Includes statement and proof of Jordan Holder Theorem. The Jordan- Holder theorem is about composition series of finite groups. The composition quotient groups belonging to two composition series of a finite group.

Provides information about: 1. Statement and proof of first isomorphism theorem. 2.Statement and proof of second isomorphism theorem. 3. Statement and proof of third isomorphism theorem. The fundamental theorem on homomorphism relates the structure of two objects between which homomorphism is given, and of the kernel and image of the homomorphism.

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