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Finite groups whose 2-subgroup...
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Finite groups whose 2-subgroups are generated by at most 4 elements / Daniel Gorenstein and Koichiro Harada.
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Bibliographic Details
Main Authors:
Gorenstein, Daniel
(Author)
,
Harada, Koichiro, 1941-
(Author)
Format:
eBook
Language:
English
Published:
Providence :
American Mathematical Society,
1974.
Series:
Memoirs of the American Mathematical Society ;
no. 147.
Subjects:
Finite groups.
Finite groups
Online Access:
Click for online access
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Description
Table of Contents
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Table of Contents:
TABLE OF CONTENTS
INTRODUCTION
PART I: SOLVABLE 2-LOCAL SUBGROUPS
1. Introduction
2. The minimal counterexample
3. Odd order groups acting on 2-groups
4. The local subgroups of G
5. The structure of O[sub(2)(M)
6. The case C[sub(R)](B) / 1
7. Proof of Theorem A
PART II: 2-CONSTRAINED 2-LOCAL SUBGROUPS
1. Introduction
2. The automorphism groups of certain 2-groups
3. Theorem B, the GL(3,2) case
4. Theorem B, the A[sub(5)]case
5. Theorems C and D, initial reduction
6. Theorems C and D, the A[sub(5)] case
7. Theorems C and D, the GL(3,2) case.
PART III: NON 2-CONSTRAINED CENTRALIZERS OF INVOLUTIONS
SOME SPECIAL CASES
1. Introduction
2. Theorem A
3. The Ŝz(8) case
4. The Â[sub(n) case
5. The M[sub(l2)] case
6. Some lemmas
7. The SL(4,q), SU(4,q), Sp(4,q) cases
8. The direct product case
9. The central product case
PART IV: A CHARACTERIZATION OF THE GROUP D[sup(2)sub(4)](3)
1. Introduction
2. Preliminary lemmas
3. The centralizer of a central involution
4. The intersection of W and its conjugates
5. The normal four subgroup case
6. The cyclic case
7. The maximal class case.
PART V: CENTRAL INVOLUTIONS WITH NON 2-CONSTRAINED CENTRALIZERS
1. Introduction
2. Initial reductions
3. Theorem A
the wreathed case
4. Preliminary results
5. Maximal elementary abelian 2-subgroups
6. Fusion of involutions
7. Theorem A
the dihedral and quasi-dihedral cases
PART VI: A CHARACTERIZATION OF THE GROUP M[sub(12)]
1. Introduction
2. 2-groups and their automorphism groups
3. Some 2-groups associated with Aut(Z[sub(4)] x Z[sub(4)])
4. Initial reductions
5. Elimination of the rank 3 case
6. The major reduction
7. The non-dihedral case.
8. The noncyclic case
9. The structure of O[sub(2)](M)
10. The structure of S.
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