94 BIBLIOGRAPHY [33] Stewart, A. G. R. <strong>On</strong> <strong>the</strong> class <strong>of</strong> certain nilpotent groups. Proc. Roy. Soc. Ser. A 292 (1966), 374–379.
APPENDIX 95 List <strong>of</strong> papers <strong>of</strong> <strong>the</strong> author 1. Juhász, T. <strong>On</strong> <strong>the</strong> derived length <strong>of</strong> <strong>Lie</strong> solvable group algebras. Publ. Math. Debrecen 68 (2006), no. 1-2, 243–256. 2. Bovdi, V.; Juhász, T.; Spinelli, E. Modular group algebras with almost maximal <strong>Lie</strong> nilpotency indices. Algebr. Represent. Theory 9 (2006), no. 3, 259-266. 3. Juhász, T. Rencent results on <strong>the</strong> derived length <strong>of</strong> <strong>Lie</strong> solvable group algebras. to appear in Acta Math. Acad. Paedagog. Nyházi. (N.S.) 22 (2006), no. 3. 4. Balogh, Zs.; Juhász, T. <strong>Lie</strong> derived lengths <strong>of</strong> group algebras <strong>of</strong> groups with cyclic derived subgroup. (submitted) List <strong>of</strong> conference talks <strong>of</strong> <strong>the</strong> author 1. The derived length <strong>of</strong> <strong>Lie</strong> soluble group algebras, International Conference on <strong>Algebras</strong>, Modules and <strong>Group</strong> Rings, July 14−18, 2003, Lisbon, Portugal. 2. A csoportalgebra <strong>Lie</strong> feloldható hossza, Országos algebra szeminárium, MTA Rényi Alfréd Matematikai Kutatóintézet, 2004. április 26., Budapest. 3. <strong>On</strong> <strong>the</strong> derived length <strong>of</strong> <strong>Lie</strong> solvable group algebras, <strong>Group</strong>s and <strong>Group</strong> Rings XI, June 4 − 11, 2005, Bedlewo, Poland. 4. <strong>On</strong> <strong>the</strong> derived length <strong>of</strong> <strong>Lie</strong> solvable group algebras, Workshop on <strong>Lie</strong> algebras, <strong>the</strong>ir classification and applications, July 25−27, 2005, Trento, Italy.
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Acknowledgements I would like to ex
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VIII CONTENTS 6 Lie nilpotency indi
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2 CHAPTER 1 of simple groups, as sp
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4 CHAPTER 1 is the so-called augmen
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6 CHAPTER 1 and for units a, b that
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8 CHAPTER 1 1.2.2 Lie derived lengt
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10 CHAPTER 1 1.2.3 Lie nilpotency i
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12 CHAPTER 2 (ii) p = 2 and G ′ i
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14 CHAPTER 2 Theorem 2.2.2. Let G b
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16 CHAPTER 2 According to Lemma 2.2
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18 CHAPTER 2
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20 CHAPTER 3 this bound is always a
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22 CHAPTER 3 and if k is even then
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24 CHAPTER 3 since γ3(G) ⊆ (G
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26 CHAPTER 3 Proof. Evidently, x =
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28 CHAPTER 3 and s > 0 the set gω
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30 CHAPTER 3 apply Lemma 3.2.4 to c
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32 CHAPTER 3 hypothesis and (3.11),
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34 CHAPTER 3 and wl+1 ≡ t (l) w t
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36 CHAPTER 3 3.2.3. Finally, let m
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38 CHAPTER 3 and char(F ) = 19. Sin
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40 CHAPTER 4 for suitable odd l. Th
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42 CHAPTER 4 Lemma 4.1.4. Let G be
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