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Finite Groups Which Are Almost Groups of Lie Type in Characteristic $\mathbf{p}$
| eBook ISBN: | 978-1-4704-7697-7 |
| Product Code: | MEMO/292/1452.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
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Finite Groups Which Are Almost Groups of Lie Type in Characteristic $\mathbf{p}$
| eBook ISBN: | 978-1-4704-7697-7 |
| Product Code: | MEMO/292/1452.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 292; 2023; 182 ppMSC: Primary 20
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminary Group Theoretical Results
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3. Identification Theorems of Some Almost Simple Groups
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4. Strongly $\mathbf {p}$-embedded Subgroups
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5. Sylow Embedded Subgroups of Linear Groups
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6. Main Hypothesis and Notation for the Proof of the Main Theorems
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7. The Embedding of $\mathbf Q$ in $\mathbf G$ Under Hypothesis
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8. The Groups Which Satisfy Hypothesis with $\mathbf { N_{F^*(H)}(Q)} $ Not Soluble and $\mathbf {N_G(Q) \not \le H}$
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9. The Groups with $\mathbf {F^*(H)\cong PSL_3(p^e)}$, $\mathbf p$ Odd
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10. The Groups with $\mathbf {F^*(H) \cong PSL_3(2^e)}$ or $\mathbf {Sp_4(2^e)’}$
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11. The Groups with $ \mathbf {F^*(H) \cong \mathbf {Sp}_{2n}(2^e)}$, $\mathbf {n \ge 3}$
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12. The Groups with $\mathbf {F^*(H)\cong {}^2F_4(2^{2e+1})^\prime }$
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13. The Groups with $\mathbf {F^*(H)\cong F_4(2^e)}$
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14. The Case When $\mathbf {p = 2}$ and Centralizer of Some $\mathbf {2}$-central Element of $\mathbf {H}$ is Soluble
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15. The Groups with $\mathbf {F^*(H) \cong G_2(3^e)}$
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16. The Groups with $\mathbf {F^*(H)\cong P\Omega ^+_8(3)}$ and $\mathbf {N_G(Q) \not \le H}$
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17. The Case When $\mathbf {p = 3}$, the Centralizer of Some $\mathbf {3}$-central Element of $\mathbf {H}$ is Soluble and $\mathbf {N_G(Q) \not \le H}$
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18. Proof of Theorem and Theorem
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19. Groups Which Satisfy Hypothesis with $\mathbf {N_G(Q) \le H}$ and Some $\mathbf {p}$-local Subgroup Containing $\mathbf {S}$ Not Contained in $\mathbf {H}$
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20. Proof of Theorem
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21. Proof of Theorem
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22. Proof of Main Theorem and Main Theorem
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A. Properties of Finite Simple Groups of Lie Type
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B. Properties Alternating Groups
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C. Small Modules for Finite Simple Groups
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D. $\mathbf {p}$-local Properties of Groups of Lie Type in Characteristic $\mathbf {p}$
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E. Miscellanea
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Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
Volume: 292; 2023; 182 pp
MSC: Primary 20
-
Chapters
-
1. Introduction
-
2. Preliminary Group Theoretical Results
-
3. Identification Theorems of Some Almost Simple Groups
-
4. Strongly $\mathbf {p}$-embedded Subgroups
-
5. Sylow Embedded Subgroups of Linear Groups
-
6. Main Hypothesis and Notation for the Proof of the Main Theorems
-
7. The Embedding of $\mathbf Q$ in $\mathbf G$ Under Hypothesis
-
8. The Groups Which Satisfy Hypothesis with $\mathbf { N_{F^*(H)}(Q)} $ Not Soluble and $\mathbf {N_G(Q) \not \le H}$
-
9. The Groups with $\mathbf {F^*(H)\cong PSL_3(p^e)}$, $\mathbf p$ Odd
-
10. The Groups with $\mathbf {F^*(H) \cong PSL_3(2^e)}$ or $\mathbf {Sp_4(2^e)’}$
-
11. The Groups with $ \mathbf {F^*(H) \cong \mathbf {Sp}_{2n}(2^e)}$, $\mathbf {n \ge 3}$
-
12. The Groups with $\mathbf {F^*(H)\cong {}^2F_4(2^{2e+1})^\prime }$
-
13. The Groups with $\mathbf {F^*(H)\cong F_4(2^e)}$
-
14. The Case When $\mathbf {p = 2}$ and Centralizer of Some $\mathbf {2}$-central Element of $\mathbf {H}$ is Soluble
-
15. The Groups with $\mathbf {F^*(H) \cong G_2(3^e)}$
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16. The Groups with $\mathbf {F^*(H)\cong P\Omega ^+_8(3)}$ and $\mathbf {N_G(Q) \not \le H}$
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17. The Case When $\mathbf {p = 3}$, the Centralizer of Some $\mathbf {3}$-central Element of $\mathbf {H}$ is Soluble and $\mathbf {N_G(Q) \not \le H}$
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18. Proof of Theorem and Theorem
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19. Groups Which Satisfy Hypothesis with $\mathbf {N_G(Q) \le H}$ and Some $\mathbf {p}$-local Subgroup Containing $\mathbf {S}$ Not Contained in $\mathbf {H}$
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20. Proof of Theorem
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21. Proof of Theorem
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22. Proof of Main Theorem and Main Theorem
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A. Properties of Finite Simple Groups of Lie Type
-
B. Properties Alternating Groups
-
C. Small Modules for Finite Simple Groups
-
D. $\mathbf {p}$-local Properties of Groups of Lie Type in Characteristic $\mathbf {p}$
-
E. Miscellanea
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