000			03733nam a22004693i 4500
001			EBC3113489
003			MiAaPQ
005			20240729124544.0
006			m o d |
007			cr cnu||||||||
008			240724s1974 xx o ||||0 eng d
020			_a9780821899472 _q(electronic bk.)
020			_z9780821818473
035			_a(MiAaPQ)EBC3113489
035			_a(Au-PeEL)EBL3113489
035			_a(CaPaEBR)ebr10882148
035			_a(OCoLC)884584175
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA177 -- .G67 1974eb
082	0		_a510/.8 s;512/.2
100	1		_aGorenstein, Daniel.
245	1	0	_aFinite Groups Whose 2-Subgroups Are Generated by at Most 4 Elements.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c1974.
264		4	_c©1974.
300			_a1 online resource (473 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.1
505	0		_aIntro -- 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).
505	8		_a10. The structure of S.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aFinite groups.
655		4	_aElectronic books.
700	1		_aHarada, Kaichiro.
776	0	8	_iPrint version: _aGorenstein, Daniel _tFinite Groups Whose 2-Subgroups Are Generated by at Most 4 Elements _dProvidence : American Mathematical Society,c1974 _z9780821818473
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3113489 _zClick to View
999			_c69023 _d69023