DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-11

How statement and proof provenance work

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.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

A finite $p$ -group has order $p^{n}$ for a prime $p$ and some $n \in N$

Definition

Let $p$ be a prime natural number (Prime and composite integers: $p$ is prime when $p > 1$ and its only positive divisors are $1$ and $p$ ). A finite $p$ -group is a finite group $P$ (Group and abelian group, The cardinality $∣ A ∣$ of a finite set) whose order has the form

$∣ P ∣ = p^{n}$

for some $n \in N$ , with natural exponentiation as in Exponentiation of natural numbers, $m^{n}$ , and its agreement with the integer power in $R$ . The case $n = 0$ permits the trivial group. A finite $p$ -group is nontrivial exactly when $n \geq 1$ .

Depends on

Dependency tree · 2 levels

Sources

K. Conrad, Group Actions, Section 4