The C12 Universal Minimality Theorem: Z₁₂ as the Smallest Cyclic Atlas Containing All Divisor Subgroups
Abstract
ABSTRACTThis paper formalizes the minimality of Z₁₂ as a universal cyclic atlas container for all cyclic groups whose orders divide 12. We prove that any cyclic group containing embedded copies of C₂, C₃, C₄, and C₆ must have order divisible by 12, and that Z₁₂ is the smallest such cyclic group. This establishes 12 as a structural consequence of divisor completeness rather than aesthetic preference.
Fields of Study & Subjects
Finite Group Theory Research
Rings
Modules
and Algebras
Mathematics and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 23 February 2026
- Language
- EN