This page is the minimal acceptance test for the bilingual finite-group-theory bundle. If the formulas, semantic blocks, table, and knowledge links below render normally, the Wikist installation provides the native Markdown and mathematics features required by the bundle. [@isaacs2008]
Inline and display mathematics
Inline mathematics should remain inside the sentence rather than appearing as source code: the symmetric group \(S_3\) has order \(|S_3|=6\), and its alternating subgroup \(A_3\) has order three.
Display mathematics should occupy its own centered line:
The orbit–stabilizer relation supplies another test:
Native semantic blocks
Knowledge links and table
The following links should open their articles rather than returning to the home page:
| Object | Order | Structure | Purpose on this page |
|---|---|---|---|
| \(A_3\) | 3 | cyclic, abelian, nilpotent | checks subscripts and inline mathematics |
| \(S_3\) | 6 | nonabelian, solvable, not nilpotent | checks theorem and proof blocks |
Structured citation
The citation marker at the end of this sentence should become an interactive reference tied to the isaacs2008 record in the page metadata. Chapter 1 of the source covers group actions, Sylow theory, and nilpotence, while Chapter 3 gives the derived-series criterion for solvability. [@isaacs2008]
This page verifies syntax integration only; it does not replace the corresponding mathematical articles. The bundle follows a tiered policy: core articles provide detailed proofs and examples, supporting articles preserve precise statements and proof references, and chapter guides audit every source number without reproducing the textbook.
