Finite groups whose 2-subgroups are generated by at most 4 elements

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
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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