This page is a verifiable reading map for Chapter 1, “Sylow Theory,” of Isaacs' Finite Group Theory. It does not reproduce the source text; it maps all 46 numbered results and 60 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 | |
|---|---|---|---|---|---|
| 1A | Group actions and coset actions | [[group-action | Group action]] | 6 | 10 |
| 1B | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | 4 | 8 |
| 1C | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | 8 | 8 |
| 1D | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | 11 | 19 |
| 1E | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | 11 | 8 |
| 1F | Problems on finite p-groups | [[p-group | p-group]] | 0 | 3 |
| 1G | Chermak–Delgado measure and characteristic abelian subgroups | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | 6 | 4 |
Numbered-result index
| Number and name | Type | Wikist article | Status | |
|---|---|---|---|---|
| Numbered result 1.1 | theorem | [[group-action | Group action]] | Topic index |
| Numbered result 1.2 | corollary | [[group-action | Group action]] | Topic index |
| Numbered result 1.3 | corollary | [[group-action | Group action]] | Topic index |
| The Fundamental Counting Principle (1.4) | theorem | [[group-action | Group action]] | Topic index |
| Numbered result 1.5 | corollary | [[group-action | Group action]] | Topic index |
| Numbered result 1.6 | corollary | [[group-action | Group action]] | Topic index |
| Sylow E (1.7) | theorem | [[sylow-theorems | Sylow theorems]] | Explicit citation |
| Numbered result 1.8 | lemma | [[sylow-theorems | Sylow theorems]] | Topic index |
| Cauchy (1.9) | corollary | [[cauchy-theorem | Cauchy's theorem]] | Explicit citation |
| Numbered result 1.10 | lemma | [[sylow-theorems | Sylow theorems]] | Topic index |
| Numbered result 1.11 | theorem | [[sylow-theorems | Sylow theorems]] | Topic index |
| Sylow C (1.12) | theorem | [[sylow-theorems | Sylow theorems]] | Explicit citation |
| Frattini Argument (1.13) | lemma | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Sylow D (1.14) | theorem | [[sylow-theorems | Sylow theorems]] | Explicit citation |
| Numbered result 1.15 | corollary | [[sylow-theorems | Sylow theorems]] | Topic index |
| Numbered result 1.16 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 1.17 | corollary | [[sylow-theorems | Sylow theorems]] | Topic index |
| Numbered result 1.18 | lemma | [[sylow-theorems | Sylow theorems]] | Topic index |
| Numbered result 1.19 | theorem | [[nilpotent-group | Nilpotent group]] | Topic index |
| Numbered result 1.20 | lemma | [[nilpotent-group | Nilpotent group]] | Topic index |
| Numbered result 1.21 | theorem | [[nilpotent-group | Nilpotent group]] | Topic index |
| Numbered result 1.22 | theorem | [[nilpotent-group | Nilpotent group]] | Topic index |
| Numbered result 1.23 | lemma | [[nilpotent-group | Nilpotent group]] | Explicit citation |
| Numbered result 1.24 | corollary | [[nilpotent-group | Nilpotent group]] | Topic index |
| Numbered result 1.25 | corollary | [[nilpotent-group | Nilpotent group]] | Explicit citation |
| Numbered result 1.26 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 1.27 | lemma | [[nilpotent-group | Nilpotent group]] | Topic index |
| Numbered result 1.28 | corollary | [[nilpotent-group | Nilpotent group]] | Topic index |
| Numbered result 1.29 | corollary | [[nilpotent-group | Nilpotent group]] | Topic index |
| Numbered result 1.30 | theorem | [[sylow-theorems | Sylow theorems]] | Explicit citation |
| Numbered result 1.31 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 1.32 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 1.33 | theorem | [[sylow-theorems | Sylow theorems]] | Topic index |
| Numbered result 1.34 | lemma | [[sylow-theorems | Sylow theorems]] | Topic index |
| Numbered result 1.35 | theorem | [[sylow-theorems | Sylow theorems]] | Topic index |
| Numbered result 1.36 | theorem | [[sylow-theorems | Sylow theorems]] | Topic index |
| Brodkey (1.37) | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 1.38 | theorem | [[sylow-theorems | Sylow theorems]] | Dedicated treatment |
| Numbered result 1.39 | corollary | [[sylow-theorems | Sylow theorems]] | Topic index |
| Numbered result 1.40 | corollary | [[sylow-theorems | Sylow theorems]] | Topic index |
| Chermak-Delgado (1.41) | theorem | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | Explicit citation |
| Numbered result 1.42 | lemma | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | Explicit citation |
| Numbered result 1.43 | lemma | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | Topic index |
| Numbered result 1.44 | theorem | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | Dedicated treatment |
| Numbered result 1.45 | corollary | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | Explicit citation |
| Numbered result 1.46 | corollary | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | 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 | |
|---|---|---|---|---|
| 1A.1 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.2 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.3 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.4 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.5 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.6 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.7 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.8 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.9 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1A.10 | Group actions and coset actions | [[group-action | Group action]] | Exercise index |
| 1B.1 | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1B.2 | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1B.3 | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1B.4 | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | Explicit citation |
| 1B.5 | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1B.6 | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1B.7 | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1B.8 | Sylow existence and Cauchy's theorem | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1C.1 | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1C.2 | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1C.3 | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1C.4 | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1C.5 | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1C.6 | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1C.7 | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1C.8 | Sylow conjugacy, counting, and the Frattini argument | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1D.1 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.2 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.3 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.4 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.5 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.6 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.7 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.8 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.9 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.10 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.11 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.12 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.13 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.14 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.15 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.16 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.17 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.18 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1D.19 | Central series, nilpotence, and Sylow decomposition | [[nilpotent-group | Nilpotent group]] | Exercise index |
| 1E.1 | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1E.2 | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1E.3 | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1E.4 | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1E.5 | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1E.6 | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1E.7 | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1E.8 | Group orders, simplicity, and Sylow applications | [[sylow-theorems | Sylow theorems]] | Exercise index |
| 1F.1 | Problems on finite p-groups | [[p-group | p-group]] | Exercise index |
| 1F.2 | Problems on finite p-groups | [[p-group | p-group]] | Exercise index |
| 1F.3 | Problems on finite p-groups | [[p-group | p-group]] | Exercise index |
| 1G.1 | Chermak–Delgado measure and characteristic abelian subgroups | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | Exercise index |
| 1G.2 | Chermak–Delgado measure and characteristic abelian subgroups | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | Exercise index |
| 1G.3 | Chermak–Delgado measure and characteristic abelian subgroups | [[chermak-delgado-subgroup | Chermak–Delgado subgroup]] | Exercise index |
| 1G.4 | Chermak–Delgado measure and characteristic abelian subgroups | [[chermak-delgado-subgroup | Chermak–Delgado 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]
