On the Derived Length of Lie Solvable Group Algebras

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Acknowledgements I would like to express my gratitude to my supervisor, Professor Béla Bódi (Adalbert Bovdi) for his magnificent ideas and his continuous encouragement during the years of the preparation of this work. I also would like to thank my colleagues, Zsolt Balogh and Viktor Bódi (Victor Bovdi) for their careful proof-reading of this work and for their advice and remarks to improve this thesis. Last but not least, I owe thank to all of my friends and my family for their extreme patience and understanding. V
Page 1: On the Derived Length of Lie Solvab
Page 7 and 8: Contents 1 Introduction 1 1.1 Preli
Page 9 and 10: Chapter 1 Introduction 1.1 Prelimin
Page 11 and 12: 1.1 PRELIMINARIES 3 Our goal in thi
Page 13 and 14: 1.2 ASSOCIATED LIE ALGEBRA OF GROUP
Page 19 and 20: Chapter 2 An extension of a result
Page 21 and 22: 2.2 THE GENERALIZED RESULT 13 Proof
Page 23 and 24: 2.2 THE GENERALIZED RESULT 15 a suf
Page 25 and 26: 2.2 THE GENERALIZED RESULT 17 As th
Page 27 and 28: Chapter 3 Lie derived lengths of gr
Page 29 and 30: 3.1 THE BASIC GROUP IS NILPOTENT 21
Page 31 and 32: 3.2 THE BASIC GROUP IS NOT NILPOTEN
Page 45 and 46: 3.3 SUMMARIZED RESULT 37 Indeed, ac
Page 47 and 48: Chapter 4 Group algebras of maximal
Page 49 and 50: 4.1 PRELIMINARIES 41 and the proof
Page 51 and 52: 4.1 PRELIMINARIES 43 for some ϱ4
Page 53 and 54: 4.2 THE DESCRIPTION AND SOME CONSEQ
Page 55 and 56:
4.2 THE DESCRIPTION AND SOME CONSEQ
Page 57 and 58:
Chapter 5 Group algebras of Lie der
Page 59 and 60:
5.1 PRELIMINARIES AND THE DESCRIPTI
Page 61 and 62:
5.1 PRELIMINARIES AND THE DESCRIPTI
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A POSSIBILITY OF APPLICATION 55 a)
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A POSSIBILITY OF APPLICATION 57 Ind
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Chapter 6 Lie nilpotency indices of
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6.1 PRELIMINARY RESULTS 61 Proposit
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GROUP ALGEBRAS WITH ALMOST MAXIMAL.
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Page 77 and 78:
Page 79 and 80:
Summary Introduction The investigat
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SUMMARY 73 Lie commutator by induct
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SUMMARY 75 commutator subgroup of t
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SUMMARY 77 Theorem. Let G be a grou
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SUMMARY 79 Theorem. Let F G be a Li
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82 sebb esetekben az egységcsoport
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84 szorzás helyett az [x, y] műve
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86 A harmadik fejezetben azon csopo
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88 (i) p = 2 és G ′ centrális n
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90 alsó Lie-nilpotencia indexének
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92 BIBLIOGRAPHY [10] Bovdi, V. Modu
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94 BIBLIOGRAPHY [33] Stewart, A. G.
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96 APPENDIX .
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On the Derived Length of Lie Solvable Group Algebras

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