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

by Gorenstein, Daniel

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Title Statements

Full title :Finite groups whose 2-subgroups are generated by at most 4 elements / Daniel Gorenstein and Koichiro Harada.

Edition Statements

Publication Date:1974.

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence
Language:eng
Publication Date:1974.

The Physical Object

Description:1 online resource (473 pages)

Edition Identifiers

ISBN:9780821899472, 0821899473
oclc:ocn884584175
LC Classification:QA177
Dewey Decimal:510/.8 s

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…