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Overgroups of Root Groups in Classical Groups
eBook ISBN:  9781470428730 
Product Code:  MEMO/241/1140.E 
List Price:  $96.00 
MAA Member Price:  $86.40 
AMS Member Price:  $57.60 
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Overgroups of Root Groups in Classical Groups
eBook ISBN:  9781470428730 
Product Code:  MEMO/241/1140.E 
List Price:  $96.00 
MAA Member Price:  $86.40 
AMS Member Price:  $57.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 241; 2015; 184 ppMSC: Primary 20
The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of croot subgroups.

Table of Contents

Chapters

Introduction

1. 3transpositions

2. The $(V,f)$setup

3. Direct sum decompositions

4. Subfield structures

5. Modules for alternating groups

6. Modules with $p=2$

7. The orthogonal space $\mathbf {F}_2^n$

8. Overgroups of long root subgroups

9. Maximal overgroups of long root subgroups

10. Subgroups containing long root elements

11. Overgroups of short root subgroups

12. Short root subgroups in symplectic groups of characteristic 2

13. Overgroups of subgroups in $\mathbf {R}_c$ in III

14. Overgroups of subgroups in $\mathbf {R}_c$ in III when $q>3$

15. A special case for $q=3$ in III

16. Overgroups of subgroups in $\mathbf {R}_c$ in III when $q=3$

17. A result of Stellmacher

18. More case III with $q=3$

19. The proof of Theorem 1

20. A characterization of alternating groups

21. Orthogonal groups with $q=2$

22. The proof of Theorem 2

23. Symplectic and unitary groups

24. Symplectic and unitary groups with $q$ odd

25. The proof of Theorem 3

26. Unitary groups with $q$ even

27. The proofs of Theorems A and B

References


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Volume: 241; 2015; 184 pp
MSC: Primary 20
The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of croot subgroups.

Chapters

Introduction

1. 3transpositions

2. The $(V,f)$setup

3. Direct sum decompositions

4. Subfield structures

5. Modules for alternating groups

6. Modules with $p=2$

7. The orthogonal space $\mathbf {F}_2^n$

8. Overgroups of long root subgroups

9. Maximal overgroups of long root subgroups

10. Subgroups containing long root elements

11. Overgroups of short root subgroups

12. Short root subgroups in symplectic groups of characteristic 2

13. Overgroups of subgroups in $\mathbf {R}_c$ in III

14. Overgroups of subgroups in $\mathbf {R}_c$ in III when $q>3$

15. A special case for $q=3$ in III

16. Overgroups of subgroups in $\mathbf {R}_c$ in III when $q=3$

17. A result of Stellmacher

18. More case III with $q=3$

19. The proof of Theorem 1

20. A characterization of alternating groups

21. Orthogonal groups with $q=2$

22. The proof of Theorem 2

23. Symplectic and unitary groups

24. Symplectic and unitary groups with $q$ odd

25. The proof of Theorem 3

26. Unitary groups with $q$ even

27. The proofs of Theorems A and B

References
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