This page is a verifiable reading map for Chapter 3, “Split Extensions,” of Isaacs' Finite Group Theory. It does not reproduce the source text; it maps all 36 numbered results and 48 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 | |
|---|---|---|---|---|---|
| 3A | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | 4 | 10 |
| 3B | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | 8 | 15 |
| 3C | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | 10 | 8 |
| 3D | Problems on solvable and supersolvable groups | [[solvable-group | Solvable group]] | 0 | 5 |
| 3E | Coprime action and Glauberman's lemma | [[coprime-action | Coprime action]] | 12 | 5 |
| 3F | Structural applications of coprime action | [[coprime-action | Coprime action]] | 2 | 5 |
Numbered-result index
| Number and name | Type | Wikist article | Status | |
|---|---|---|---|---|
| Numbered result 3.1 | lemma | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 3.2 | theorem | [[automorphism-tower | Automorphism tower]] | Topic index |
| Horosevskii (3.3) | corollary | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 3.4 | corollary | [[automorphism-tower | Automorphism tower]] | Topic index |
| Numbered result 3.5 | theorem | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Explicit citation |
| Numbered result 3.6 | lemma | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Topic index |
| Numbered result 3.7 | lemma | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Explicit citation |
| Numbered result 3.8 | theorem | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Topic index |
| Numbered result 3.9 | lemma | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Topic index |
| Numbered result 3.10 | lemma | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Topic index |
| Numbered result 3.11 | lemma | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Topic index |
| Numbered result 3.12 | theorem | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Explicit citation |
| Hall-E (3.13) | theorem | [[hall-subgroup | Hall subgroup]] | Dedicated treatment |
| Hall-C (3.14) | theorem | [[hall-subgroup | Hall subgroup]] | Dedicated treatment |
| Numbered result 3.15 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 3.16 | lemma | [[hall-subgroup | Hall subgroup]] | Topic index |
| Numbered result 3.17 | theorem | [[hall-subgroup | Hall subgroup]] | Topic index |
| Numbered result 3.18 | lemma | [[hall-subgroup | Hall subgroup]] | Topic index |
| Numbered result 3.19 | corollary | [[hall-subgroup | Hall subgroup]] | Topic index |
| Numbered result 3.20 | theorem | [[hall-subgroup | Hall subgroup]] | Topic index |
| Hall-Higman 1.2.3 (3.21) | theorem | [[hall-subgroup | Hall subgroup]] | Topic index |
| Numbered result 3.22 | theorem | [[hall-subgroup | Hall subgroup]] | Topic index |
| Numbered result 3.23 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Glauberman (3.24) | lemma | [[glauberman-lemma | Glauberman lemma]] | Dedicated treatment |
| Numbered result 3.25 | corollary | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 3.26 | theorem | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.27 | theorem | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.28 | corollary | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.29 | corollary | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.30 | corollary | [[coprime-action | Coprime action]] | Topic index |
| Hartley-Turull (3.31) | theorem | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.32 | lemma | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.33 | lemma | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.34 | theorem | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.35 | theorem | [[coprime-action | Coprime action]] | Topic index |
| Numbered result 3.36 | theorem | [[coprime-action | Coprime action]] | 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 | |
|---|---|---|---|---|
| 3A.1 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.2 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.3 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.4 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.5 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.6 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.7 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.8 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.9 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3A.10 | Orders of automorphisms of finite groups | [[automorphism-tower | Automorphism tower]] | Exercise index |
| 3B.1 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.2 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.3 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.4 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.5 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.6 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.7 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.8 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.9 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.10 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.11 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.12 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.13 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.14 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3B.15 | Schur–Zassenhaus and solvable groups | [[schur-zassenhaus-theorem | Schur–Zassenhaus theorem]] | Exercise index |
| 3C.1 | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | Exercise index |
| 3C.2 | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | Exercise index |
| 3C.3 | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | Exercise index |
| 3C.4 | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | Exercise index |
| 3C.5 | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | Exercise index |
| 3C.6 | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | Exercise index |
| 3C.7 | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | Exercise index |
| 3C.8 | Hall theory for finite solvable groups | [[hall-subgroup | Hall subgroup]] | Exercise index |
| 3D.1 | Problems on solvable and supersolvable groups | [[solvable-group | Solvable group]] | Exercise index |
| 3D.2 | Problems on solvable and supersolvable groups | [[solvable-group | Solvable group]] | Exercise index |
| 3D.3 | Problems on solvable and supersolvable groups | [[solvable-group | Solvable group]] | Exercise index |
| 3D.4 | Problems on solvable and supersolvable groups | [[solvable-group | Solvable group]] | Exercise index |
| 3D.5 | Problems on solvable and supersolvable groups | [[solvable-group | Solvable group]] | Exercise index |
| 3E.1 | Coprime action and Glauberman's lemma | [[coprime-action | Coprime action]] | Exercise index |
| 3E.2 | Coprime action and Glauberman's lemma | [[coprime-action | Coprime action]] | Exercise index |
| 3E.3 | Coprime action and Glauberman's lemma | [[coprime-action | Coprime action]] | Exercise index |
| 3E.4 | Coprime action and Glauberman's lemma | [[coprime-action | Coprime action]] | Exercise index |
| 3E.5 | Coprime action and Glauberman's lemma | [[coprime-action | Coprime action]] | Exercise index |
| 3F.1 | Structural applications of coprime action | [[coprime-action | Coprime action]] | Exercise index |
| 3F.2 | Structural applications of coprime action | [[coprime-action | Coprime action]] | Exercise index |
| 3F.3 | Structural applications of coprime action | [[coprime-action | Coprime action]] | Exercise index |
| 3F.4 | Structural applications of coprime action | [[coprime-action | Coprime action]] | Exercise index |
| 3F.5 | Structural applications of coprime action | [[coprime-action | Coprime action]] | 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]
