This page is a verifiable reading map for Chapter 4, “Commutators,” of Isaacs' Finite Group Theory. It does not reproduce the source text; it maps all 38 numbered results and 28 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 | |
|---|---|---|---|---|---|
| 4A | Commutator calculus | [[commutator | Commutator]] | 8 | 13 |
| 4B | Three-subgroup methods and commutator identities | [[three-subgroups-lemma | Three-subgroups lemma]] | 11 | 5 |
| 4C | Special p-groups and power structure | [[extraspecial-p-group | Extraspecial p-group]] | 8 | 3 |
| 4D | The Fitting subgroup and normal nilpotent structure | [[fitting-subgroup | Fitting subgroup]] | 11 | 7 |
Numbered-result index
| Number and name | Type | Wikist article | Status | |
|---|---|---|---|---|
| Numbered result 4.1 | lemma | [[commutator | Commutator]] | Topic index |
| Numbered result 4.2 | lemma | [[commutator | Commutator]] | Topic index |
| Numbered result 4.3 | lemma | [[commutator | Commutator]] | Topic index |
| Numbered result 4.4 | lemma | [[commutator | Commutator]] | Topic index |
| Numbered result 4.5 | lemma | [[commutator | Commutator]] | Topic index |
| Numbered result 4.6 | lemma | [[commutator | Commutator]] | Explicit citation |
| Numbered result 4.7 | theorem | [[commutator | Commutator]] | Topic index |
| Numbered result 4.8 | theorem | [[commutator | Commutator]] | Topic index |
| Numbered result 4.9 | lemma | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.10 | corollary | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.11 | theorem | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.12 | corollary | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.13 | corollary | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Mann (4.14) | theorem | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.15 | theorem | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.16 | lemma | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.17 | lemma | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.18 | corollary | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.19 | theorem | [[three-subgroups-lemma | Three-subgroups lemma]] | Topic index |
| Numbered result 4.20 | lemma | [[extraspecial-p-group | Extraspecial p-group]] | Topic index |
| Numbered result 4.21 | corollary | [[extraspecial-p-group | Extraspecial p-group]] | Topic index |
| Numbered result 4.22 | theorem | [[extraspecial-p-group | Extraspecial p-group]] | Topic index |
| Numbered result 4.23 | corollary | [[extraspecial-p-group | Extraspecial p-group]] | Topic index |
| Numbered result 4.24 | theorem | [[extraspecial-p-group | Extraspecial p-group]] | Topic index |
| Numbered result 4.25 | lemma | [[extraspecial-p-group | Extraspecial p-group]] | Topic index |
| Numbered result 4.26 | theorem | [[extraspecial-p-group | Extraspecial p-group]] | Topic index |
| Numbered result 4.27 | theorem | [[extraspecial-p-group | Extraspecial p-group]] | Topic index |
| Numbered result 4.28 | lemma | [[fitting-subgroup | Fitting subgroup]] | Topic index |
| Numbered result 4.29 | lemma | [[fitting-subgroup | Fitting subgroup]] | Topic index |
| Numbered result 4.30 | corollary | [[fitting-subgroup | Fitting subgroup]] | Topic index |
| Thompson (4.31) | theorem | [[thompson-subgroup | Thompson subgroup]] | Dedicated treatment |
| Numbered result 4.32 | lemma | [[fitting-subgroup | Fitting subgroup]] | Topic index |
| Numbered result 4.33 | theorem | [[fitting-subgroup | Fitting subgroup]] | Topic index |
| Fitting (4.34) | theorem | [[fitting-subgroup | Fitting subgroup]] | Dedicated treatment |
| Numbered result 4.35 | corollary | [[fitting-subgroup | Fitting subgroup]] | Topic index |
| Numbered result 4.36 | theorem | [[fitting-subgroup | Fitting subgroup]] | Topic index |
| Baer trick (4.37) | lemma | [[fitting-subgroup | Fitting subgroup]] | Topic index |
| Numbered result 4.38 | theorem | [[fitting-subgroup | Fitting 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 | |
|---|---|---|---|---|
| 4A.1 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.2 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.3 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.4 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.5 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.6 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.7 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.8 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.9 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.10 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.11 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.12 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4A.13 | Commutator calculus | [[commutator | Commutator]] | Exercise index |
| 4B.1 | Three-subgroup methods and commutator identities | [[three-subgroups-lemma | Three-subgroups lemma]] | Exercise index |
| 4B.2 | Three-subgroup methods and commutator identities | [[three-subgroups-lemma | Three-subgroups lemma]] | Exercise index |
| 4B.3 | Three-subgroup methods and commutator identities | [[three-subgroups-lemma | Three-subgroups lemma]] | Exercise index |
| 4B.4 | Three-subgroup methods and commutator identities | [[three-subgroups-lemma | Three-subgroups lemma]] | Exercise index |
| 4B.5 | Three-subgroup methods and commutator identities | [[three-subgroups-lemma | Three-subgroups lemma]] | Exercise index |
| 4C.1 | Special p-groups and power structure | [[extraspecial-p-group | Extraspecial p-group]] | Exercise index |
| 4C.2 | Special p-groups and power structure | [[extraspecial-p-group | Extraspecial p-group]] | Exercise index |
| 4C.3 | Special p-groups and power structure | [[extraspecial-p-group | Extraspecial p-group]] | Exercise index |
| 4D.1 | The Fitting subgroup and normal nilpotent structure | [[fitting-subgroup | Fitting subgroup]] | Exercise index |
| 4D.2 | The Fitting subgroup and normal nilpotent structure | [[fitting-subgroup | Fitting subgroup]] | Exercise index |
| 4D.3 | The Fitting subgroup and normal nilpotent structure | [[fitting-subgroup | Fitting subgroup]] | Exercise index |
| 4D.4 | The Fitting subgroup and normal nilpotent structure | [[fitting-subgroup | Fitting subgroup]] | Exercise index |
| 4D.5 | The Fitting subgroup and normal nilpotent structure | [[fitting-subgroup | Fitting subgroup]] | Exercise index |
| 4D.6 | The Fitting subgroup and normal nilpotent structure | [[fitting-subgroup | Fitting subgroup]] | Exercise index |
| 4D.7 | The Fitting subgroup and normal nilpotent structure | [[fitting-subgroup | Fitting 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]
