This page is a verifiable reading map for Chapter 5, “Transfer,” of Isaacs' Finite Group Theory. It does not reproduce the source text; it maps all 29 numbered results and 33 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 | |
|---|---|---|---|---|---|
| 5A | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | 4 | 8 |
| 5B | Evaluation and kernels of transfer | [[transfer-homomorphism | Transfer homomorphism]] | 5 | 3 |
| 5C | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | 9 | 13 |
| 5D | The focal subgroup and control of fusion | [[focal-subgroup-theorem | Focal subgroup theorem]] | 5 | 6 |
| 5E | Frobenius' normal p-complement theorem | [[frobenius-normal-p-complement-theorem | Frobenius normal p-complement theorem]] | 6 | 3 |
Numbered-result index
| Number and name | Type | Wikist article | Status | |
|---|---|---|---|---|
| Numbered result 5.1 | theorem | [[transfer-homomorphism | Transfer homomorphism]] | Explicit citation |
| Numbered result 5.2 | theorem | [[transfer-homomorphism | Transfer homomorphism]] | Explicit citation |
| Numbered result 5.3 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 5.4 | corollary | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Transfer Evaluation (5.5) | lemma | [[transfer-homomorphism | Transfer homomorphism]] | Dedicated treatment |
| Numbered result 5.6 | theorem | [[transfer-homomorphism | Transfer homomorphism]] | Topic index |
| Schur (5.7) | theorem | [[transfer-homomorphism | Transfer homomorphism]] | Topic index |
| Numbered result 5.9 | corollary | [[transfer-homomorphism | Transfer homomorphism]] | Topic index |
| Dietzmann (5.10) | theorem | [[transfer-homomorphism | Transfer homomorphism]] | Topic index |
| Numbered result 5.11 | lemma | [[normal-p-complement | Normal p-complement]] | Topic index |
| Numbered result 5.12 | lemma | [[normal-p-complement | Normal p-complement]] | Topic index |
| Burnside (5.13) | theorem | [[burnside-paqb-theorem | Burnside paqb theorem]] | Dedicated treatment |
| Numbered result 5.14 | corollary | [[normal-p-complement | Normal p-complement]] | Topic index |
| Numbered result 5.15 | corollary | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 5.16 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 5.17 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 5.18 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 5.19 | corollary | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 5.20 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Focal Subgroup (5.21) | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 5.22 | corollary | [[focal-subgroup-theorem | Focal subgroup theorem]] | Topic index |
| Numbered result 5.23 | corollary | [[focal-subgroup-theorem | Focal subgroup theorem]] | Topic index |
| Numbered result 5.24 | theorem | [[focal-subgroup-theorem | Focal subgroup theorem]] | Topic index |
| Numbered result 5.25 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Frobenius (5.26) | theorem | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 5.27 | lemma | [[frobenius-normal-p-complement-theorem | Frobenius normal p-complement theorem]] | Topic index |
| Numbered result 5.28 | lemma | [[frobenius-normal-p-complement-theorem | Frobenius normal p-complement theorem]] | Topic index |
| Numbered result 5.29 | corollary | [[thompson-subgroup | Thompson subgroup]] | Dedicated treatment |
| Numbered result 5.30 | corollary | [[frobenius-normal-p-complement-theorem | Frobenius normal p-complement theorem]] | 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 | |
|---|---|---|---|---|
| 5A.1 | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5A.2 | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5A.3 | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5A.4 | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5A.5 | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5A.6 | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5A.7 | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5A.8 | Pretransfer and the transfer homomorphism | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5B.1 | Evaluation and kernels of transfer | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5B.2 | Evaluation and kernels of transfer | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5B.3 | Evaluation and kernels of transfer | [[transfer-homomorphism | Transfer homomorphism]] | Exercise index |
| 5C.1 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.2 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.3 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.4 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.5 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.6 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.7 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.8 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.9 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.10 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.11 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.12 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5C.13 | Burnside and Tate normal p-complement criteria | [[normal-p-complement | Normal p-complement]] | Exercise index |
| 5D.1 | The focal subgroup and control of fusion | [[focal-subgroup-theorem | Focal subgroup theorem]] | Exercise index |
| 5D.2 | The focal subgroup and control of fusion | [[focal-subgroup-theorem | Focal subgroup theorem]] | Exercise index |
| 5D.3 | The focal subgroup and control of fusion | [[focal-subgroup-theorem | Focal subgroup theorem]] | Exercise index |
| 5D.4 | The focal subgroup and control of fusion | [[focal-subgroup-theorem | Focal subgroup theorem]] | Exercise index |
| 5D.5 | The focal subgroup and control of fusion | [[focal-subgroup-theorem | Focal subgroup theorem]] | Exercise index |
| 5D.6 | The focal subgroup and control of fusion | [[focal-subgroup-theorem | Focal subgroup theorem]] | Exercise index |
| 5E.1 | Frobenius' normal p-complement theorem | [[frobenius-normal-p-complement-theorem | Frobenius normal p-complement theorem]] | Exercise index |
| 5E.2 | Frobenius' normal p-complement theorem | [[frobenius-normal-p-complement-theorem | Frobenius normal p-complement theorem]] | Exercise index |
| 5E.3 | Frobenius' normal p-complement theorem | [[frobenius-normal-p-complement-theorem | Frobenius normal p-complement theorem]] | 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]
