Ballester-Bolinches A. Products of finite groups (Berlin; New York, 2010). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаBallester-Bolinches A. Products of finite groups / A.Ballester-Bolinches, R.Esteban-Romero, M.Asaad. - Berlin; New York: De Gruyter, 2010. - xii, 334 p.: ill. - (De Gruyter expositions in mathematics; 53). - Bibliogr.: p.303-317. - Ind.: p.323-329. - Ind. of names: p.331-334. - ISBN 978-3-11-020417-9; ISSN 0938-6572
 

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Оглавление / Contents
 
Preface ....................................................... vii
1  Prerequisites ................................................ 1
   1.1  Factorised groups - basic concepts ...................... 1
   1.2  Permutability, Sylow permutability, and related
        properties ............................................. 10
   1.3  Power automorphisms .................................... 22
   1.4  Dedekind and Iwasawa groups ............................ 24
   1.5  Pronormality, weak normality, and the subnormaliser
        condition .............................................. 26
   1.6  SC-groups .............................................. 31
   1.7  Numerical invariants of π-soluble groups ............... 35
2  Groups whose subnormal subgroups are normal, permutable, 
   or Sylow-permutable ......................................... 52
   2.1  Characterisations based on the normal structure ........ 54
   2.2  Local characterisations ................................ 67
   2.3  Characterisations based on subgroup embedding
        properties ............................................. 79
   2.4  Chief factors of PST-groups ............................ 85
3  Products of nilpotent groups ................................ 92
   3.1  Products of abelian groups ............................. 93
   3.2  The subgroup structure of a dinilpotent group ......... 100
   3.3  Numerical invariants of dinilpotent groups ............ 118
4  Totally and mutually permutable products of groups - 
   structural results ......................................... 149
   4.1  Elementary properties ................................. 151
   4.2  Nilpotent and supersoluble residuals of totally
        permutable products ................................... 172
   4.3  Minimal normal subgroups and nilpotent and soluble
        residuals of mutually permutable products ............. 184
   4.4  Mutually permutable products: residuals and
        radicals .............................................. 199
   4.5  Mutually permutable products: the core-free
        intersection case ..................................... 216
5  Totally and mutually permutable products and classes of
   groups ..................................................... 227
   5.1  Totally and mutually permutable products of
        nilpotent groups ...................................... 227
   5.2  Totally and mutually permutable products and
        formation subgroups ................................... 252
   5.3  Totally permutable products and Fitting classes ....... 270
   5.4  Mutually permutable products and other classes of
        groups ................................................ 292
   5.5  Concluding remarks .................................... 300
   References ................................................. 303
List of symbols ............................................... 319
Index ......................................................... 323
Index of names ................................................ 331


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