Alphabeta MathFinite Abelian Groups: Examples and Counterexamples
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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✓ 8 results · all verified · 0 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 8 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Abstract Algebra
Number Theory
Real Analysis
2 · Logical flowchart
3 · Items
Example
The cyclic group of order six in elementary-divisor and invariant-factor forms
Example
The five abelian groups of order sixteen
Example
Successive p-multiple layers recover the summands of Cₚ² times C_p³ times C_p⁴²
Example
The six abelian groups of order 360 in both classification forms
Example
Complements of a maximal cyclic subgroup in Cₚ× Cₚ need not be unique
Example
The unit group modulo one hundred is isomorphic to C₂₀ × C₂
Counterexample
The additive rationals do not decompose as a product of finite cyclic prime-power groups
False statement