## Subnormal Subgroups of GroupsThis book is the first to give a comprehensive account of subnormal subgroups of both finite and infinite groups. The authors trace the historical development of the subject from the early work of Wielandt, including the celebrated "join problem," to very recent results relating to the elusive subnormalizer of a subgroup. The book explains how the study of group rings can give a powerful and unified approach to major problems and encourages postgraduates and researchers in group theory and ring theory to further explore problems whose solutions remain incomplete. |

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### Contents

INDEX OF NOTATION | 11 |

THE JOIN OF MANY SUBNORMAL SUBGROUPS | 42 |

THE DERIVED AND LOWER CENTRAL SERIES OF | 89 |

Copyright | |

5 other sections not shown

### Common terms and phrases

abelian abelian group apply argument ascending assume bounded central choose clear Clearly commutators composition condition conjugates consider contained contradiction Corollary course cyclic deduce defect define denote depends derived divisible easy elements example exists fact factors Finally finite group finite rank finitely generated subgroup follows function further give given group G H sn G Hence holds homomorphism hypercentral implies induction induction hypothesis infinite join Lemma length Let G Let H locally maximal Min-sn minimal natural nilpotent groups non-trivial normal closure normal subgroup obtain once operators p-group perfect periodic permutable subgroup prime proceed proof of Theorem proper Proposition prove Remark respectively result satisfies Similarly simple soluble soluble groups subgroup of G subgroups H subnormal in G subnormal subgroups sufficient Suppose that G Sylow p-subgroup term Wielandt write