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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