This page is a verifiable reading map for Chapter 6, “Frobenius Actions,” of Isaacs' Finite Group Theory. It does not reproduce the source text; it maps all 24 numbered results and 22 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 | |
|---|---|---|---|---|---|
| 6A | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | 7 | 11 |
| 6B | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | 14 | 9 |
| 6C | Thompson's normal p-complement method | [[thompson-subgroup | Thompson subgroup]] | 3 | 2 |
Numbered-result index
| Number and name | Type | Wikist article | Status | |
|---|---|---|---|---|
| Numbered result 6.1 | lemma | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.2 | corollary | [[frobenius-group | Frobenius group]] | Explicit citation |
| Numbered result 6.3 | theorem | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.4 | theorem | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.5 | lemma | [[frobenius-group | Frobenius group]] | Topic index |
| Numbered result 6.6 | corollary | [[frobenius-group | Frobenius group]] | Topic index |
| Numbered result 6.7 | theorem | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.8 | lemma | [[frobenius-kernel | Frobenius kernel]] | Topic index |
| Numbered result 6.9 | theorem | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.10 | corollary | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.11 | theorem | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.12 | theorem | [[frobenius-kernel | Frobenius kernel]] | Topic index |
| Numbered result 6.13 | lemma | [[frobenius-kernel | Frobenius kernel]] | Topic index |
| Numbered result 6.14 | corollary | [[frobenius-kernel | Frobenius kernel]] | Topic index |
| Numbered result 6.15 | lemma | [[frobenius-kernel | Frobenius kernel]] | Topic index |
| Numbered result 6.16 | lemma | [[frobenius-kernel | Frobenius kernel]] | Topic index |
| Numbered result 6.17 | corollary | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 6.18 | corollary | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.19 | theorem | [[frobenius-group | Frobenius group]] | Dedicated treatment |
| Numbered result 6.20 | lemma | [[frobenius-kernel | Frobenius kernel]] | Topic index |
| Numbered result 6.21 | theorem | [[frobenius-kernel | Frobenius kernel]] | Topic index |
| Numbered result 6.22 | theorem | [[frobenius-group | Frobenius group]] | Explicit citation |
| Thompson (6.23) | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 6.24 | theorem | [[frobenius-group | Frobenius group]] | Explicit citation |
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 | |
|---|---|---|---|---|
| 6A.1 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.2 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.3 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.4 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.5 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.6 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.7 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.8 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.9 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.10 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6A.11 | Frobenius actions and Frobenius groups | [[frobenius-group | Frobenius group]] | Exercise index |
| 6B.1 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6B.2 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6B.3 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6B.4 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6B.5 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6B.6 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6B.7 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6B.8 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6B.9 | Frobenius kernels, complements, and fixed-point-free action | [[frobenius-kernel | Frobenius kernel]] | Exercise index |
| 6C.1 | Thompson's normal p-complement method | [[thompson-subgroup | Thompson subgroup]] | Exercise index |
| 6C.2 | Thompson's normal p-complement method | [[thompson-subgroup | Thompson 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]
