This page is a verifiable reading map for Chapter 8, “Permutation Groups,” of Isaacs' Finite Group Theory. It does not reproduce the source text; it maps all 43 numbered results and 39 problems to the core or supporting Wikist articles that carry the explanation. [@isaacs2008]
How to use this guide
Section navigation
| Section | Topic | Target article | Results | Problems | |
|---|---|---|---|---|---|
| 8A | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | 9 | 17 |
| 8B | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | 16 | 10 |
| 8C | Projective special linear groups and simplicity | [[projective-special-linear-group | Projective special linear group]] | 7 | 6 |
| 8D | Orbital graphs and subdegrees | [[orbital-graph | Orbital graph]] | 11 | 6 |
Numbered-result index
| Number and name | Type | Wikist article | Status | |
|---|---|---|---|---|
| Numbered result 8.1 | lemma | [[permutation-group | Permutation group]] | Topic index |
| Numbered result 8.3 | lemma | [[permutation-group | Permutation group]] | Topic index |
| Numbered result 8.4 | corollary | [[permutation-group | Permutation group]] | Topic index |
| Numbered result 8.5 | lemma | [[permutation-group | Permutation group]] | Topic index |
| Numbered result 8.6 | corollary | [[permutation-group | Permutation group]] | Topic index |
| Numbered result 8.7 | corollary | [[permutation-group | Permutation group]] | Topic index |
| Numbered result 8.8 | lemma | [[permutation-group | Permutation group]] | Topic index |
| Numbered result 8.9 | theorem | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 8.10 | lemma | [[permutation-group | Permutation group]] | Topic index |
| Numbered result 8.11 | lemma | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.12 | corollary | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.13 | lemma | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.14 | corollary | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.15 | lemma | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.16 | lemma | [[primitive-action | Primitive action]] | Topic index |
| Jordan (8.17) | theorem | [[primitive-action | Primitive action]] | Topic index |
| Jordan (8.18) | theorem | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.19 | corollary | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.20 | lemma | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.21 | lemma | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.22 | theorem | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.23 | theorem | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.24 | lemma | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.25 | lemma | [[primitive-action | Primitive action]] | Topic index |
| Bochert (8.26) | theorem | [[primitive-action | Primitive action]] | Topic index |
| Numbered result 8.27 | theorem | [[projective-special-linear-group | Projective special linear group]] | Topic index |
| Numbered result 8.28 | corollary | [[projective-special-linear-group | Projective special linear group]] | Topic index |
| Numbered result 8.29 | lemma | [[projective-special-linear-group | Projective special linear group]] | Explicit citation |
| Iwasawa (8.30) | lemma | [[simplicity-of-psl | Simplicity of projective special linear groups]] | Explicit citation |
| Numbered result 8.31 | theorem | [[projective-special-linear-group | Projective special linear group]] | Topic index |
| Numbered result 8.32 | theorem | [[projective-special-linear-group | Projective special linear group]] | Topic index |
| Numbered result 8.33 | theorem | [[projective-special-linear-group | Projective special linear group]] | Explicit citation |
| Numbered result 8.34 | lemma | [[orbital-graph | Orbital graph]] | Explicit citation |
| Numbered result 8.35 | theorem | [[orbital-graph | Orbital graph]] | Topic index |
| Numbered result 8.36 | lemma | [[orbital-graph | Orbital graph]] | Topic index |
| Numbered result 8.37 | theorem | [[orbital-graph | Orbital graph]] | Topic index |
| Weiss (8.38) | theorem | [[orbital-graph | Orbital graph]] | Topic index |
| Numbered result 8.39 | lemma | [[orbital-graph | Orbital graph]] | Topic index |
| Manning (8.40) | theorem | [[orbital-graph | Orbital graph]] | Topic index |
| Numbered result 8.41 | theorem | [[orbital-graph | Orbital graph]] | Topic index |
| Numbered result 8.42 | theorem | [[orbital-graph | Orbital graph]] | Topic index |
| Numbered result 8.43 | theorem | [[orbital-graph | Orbital graph]] | Explicit citation |
| Numbered result 8.44 | corollary | [[orbital-graph | Orbital graph]] | Topic index |
Problem knowledge index
The table locates every problem at its main knowledge node. It does not disguise solutions as encyclopedia prose; exercise material that has been extracted into a theorem or structural consequence is identified in the target article.
| Problem | Section topic | Wikist article | Status | |
|---|---|---|---|---|
| 8A.1 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.2 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.3 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.4 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.5 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.6 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.7 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.8 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.9 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.10 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.11 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.12 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.13 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.14 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.15 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.16 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8A.17 | Transitive and primitive permutation groups | [[permutation-group | Permutation group]] | Exercise index |
| 8B.1 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.2 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.3 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.4 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.5 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.6 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.7 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.8 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.9 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8B.10 | Multiple transitivity, suborbits, and stabilizers | [[primitive-action | Primitive action]] | Exercise index |
| 8C.1 | Projective special linear groups and simplicity | [[projective-special-linear-group | Projective special linear group]] | Exercise index |
| 8C.2 | Projective special linear groups and simplicity | [[projective-special-linear-group | Projective special linear group]] | Exercise index |
| 8C.3 | Projective special linear groups and simplicity | [[projective-special-linear-group | Projective special linear group]] | Exercise index |
| 8C.4 | Projective special linear groups and simplicity | [[projective-special-linear-group | Projective special linear group]] | Exercise index |
| 8C.5 | Projective special linear groups and simplicity | [[projective-special-linear-group | Projective special linear group]] | Exercise index |
| 8C.6 | Projective special linear groups and simplicity | [[projective-special-linear-group | Projective special linear group]] | Exercise index |
| 8D.1 | Orbital graphs and subdegrees | [[orbital-graph | Orbital graph]] | Exercise index |
| 8D.2 | Orbital graphs and subdegrees | [[orbital-graph | Orbital graph]] | Exercise index |
| 8D.3 | Orbital graphs and subdegrees | [[orbital-graph | Orbital graph]] | Exercise index |
| 8D.4 | Orbital graphs and subdegrees | [[orbital-graph | Orbital graph]] | Exercise index |
| 8D.5 | Orbital graphs and subdegrees | [[orbital-graph | Orbital graph]] | Exercise index |
| 8D.6 | Orbital graphs and subdegrees | [[orbital-graph | Orbital graph]] | Exercise index |
Quality boundary
This guide provides complete navigation rather than replacing the source. Core articles include principal proofs; supporting articles give precise statements, boundaries, examples, and proof references. Items marked as topic or exercise indexes retain their source locations in the coverage manifest and can be promoted to standalone articles through community review. [@isaacs2008]
