This page is a verifiable reading map for Chapter 9, “More on Subnormality,” of Isaacs' Finite Group Theory. It does not reproduce the source text; it maps all 31 numbered results and 20 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 | |
|---|---|---|---|---|---|
| 9A | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | 9 | 8 |
| 9B | Automorphism towers and Wielandt methods | [[automorphism-tower | Automorphism tower]] | 13 | 5 |
| 9C | The Thompson–Wielandt theorem | [[thompson-wielandt-theorem | Thompson–Wielandt theorem]] | 5 | 3 |
| 9D | Advanced subnormality | [[subnormal-subgroup | Subnormal subgroup]] | 4 | 4 |
Numbered-result index
| Number and name | Type | Wikist article | Status | |
|---|---|---|---|---|
| Numbered result 9.1 | lemma | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Numbered result 9.2 | lemma | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Numbered result 9.3 | lemma | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Numbered result 9.4 | theorem | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Numbered result 9.5 | lemma | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Numbered result 9.6 | lemma | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Numbered result 9.7 | theorem | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Numbered result 9.8 | theorem | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Numbered result 9.9 | corollary | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Topic index |
| Wielandt (9.10) | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 9.11 | lemma | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.12 | lemma | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.13 | theorem | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.14 | lemma | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.15 | lemma | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.16 | corollary | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.17 | lemma | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.18 | corollary | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.19 | lemma | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.20 | lemma | [[automorphism-tower | Automorphism tower]] | Topic index |
| Schenkman (9.21) | theorem | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 9.22 | theorem | [[automorphism-tower | Automorphism tower]] | Explicit citation |
| Thompson (9.23) | theorem | [[thompson-subgroup | Thompson subgroup]] | Dedicated treatment |
| Numbered result 9.24 | theorem | [[thompson-wielandt-theorem | Thompson–Wielandt theorem]] | Explicit citation |
| Numbered result 9.25 | lemma | [[thompson-wielandt-theorem | Thompson–Wielandt theorem]] | Topic index |
| Numbered result 9.26 | lemma | [[thompson-wielandt-theorem | Thompson–Wielandt theorem]] | Topic index |
| Numbered result 9.27 | corollary | [[thompson-wielandt-theorem | Thompson–Wielandt theorem]] | Topic index |
| Bartels (9.28) | theorem | [[subnormal-subgroup | Subnormal subgroup]] | Topic index |
| Numbered result 9.29 | lemma | [[subnormal-subgroup | Subnormal subgroup]] | Topic index |
| Numbered result 9.30 | lemma | [[subnormal-subgroup | Subnormal subgroup]] | Topic index |
| Numbered result 9.31 | lemma | [[subnormal-subgroup | Subnormal subgroup]] | 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 | |
|---|---|---|---|---|
| 9A.1 | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Exercise index |
| 9A.2 | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Exercise index |
| 9A.3 | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Exercise index |
| 9A.4 | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Exercise index |
| 9A.5 | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Exercise index |
| 9A.6 | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Exercise index |
| 9A.7 | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Exercise index |
| 9A.8 | Quasisimple components and the generalized Fitting subgroup | [[generalized-fitting-subgroup | Generalized Fitting subgroup]] | Exercise index |
| 9B.1 | Automorphism towers and Wielandt methods | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 9B.2 | Automorphism towers and Wielandt methods | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 9B.3 | Automorphism towers and Wielandt methods | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 9B.4 | Automorphism towers and Wielandt methods | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 9B.5 | Automorphism towers and Wielandt methods | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 9C.1 | The Thompson–Wielandt theorem | [[thompson-wielandt-theorem | Thompson–Wielandt theorem]] | Exercise index |
| 9C.2 | The Thompson–Wielandt theorem | [[thompson-wielandt-theorem | Thompson–Wielandt theorem]] | Exercise index |
| 9C.3 | The Thompson–Wielandt theorem | [[thompson-wielandt-theorem | Thompson–Wielandt theorem]] | Exercise index |
| 9D.1 | Advanced subnormality | [[subnormal-subgroup | Subnormal subgroup]] | Exercise index |
| 9D.2 | Advanced subnormality | [[subnormal-subgroup | Subnormal subgroup]] | Exercise index |
| 9D.3 | Advanced subnormality | [[subnormal-subgroup | Subnormal subgroup]] | Exercise index |
| 9D.4 | Advanced subnormality | [[subnormal-subgroup | Subnormal subgroup]] | 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]
