On The Group Isomorphism Of Discrete Bravais Tori

Key Points

• The aim is to rigorously analyze the algebraic structure of discrete Bravais tori using Born-Von Karman boundary conditions.
• Defined the Bravais lattice and its properties.
• Constructed the isomorphism between the finite discrete torus and the product of cyclic groups.
• Applied the First Isomorphism Theorem to establish key relationships.
• Introduced the concept of the Born-Von Karman Fundamental Cell as a transversal of the discrete torus.
• Established a clear isomorphism between discrete Bravais tori and cyclic groups.
• Validated the use of the First Isomorphism Theorem as a key method in the proof.
• Defined a new transversality concept through the Born-Von Karman Fundamental Cell.

Abstract