1999
DOI: 10.1006/jabr.1998.7617
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Lie Properties of the Group Algebra and the Nilpotency Class of the Group of Units

Abstract: We describe the upper and lower Lie nilpotency index of a modular group algebra ‫ކ‬G of some metabelian group G and apply these results to determine the nilpotency class of the group of units, extending certain results of Shalev without restriction to finite groups. A characterization of modular group algebras ‫ކ‬G with group of units of class 3 is given, which was obtained by Rao and Sandling for finite groups G. ᮊ

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Cited by 39 publications
(40 citation statements)
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“…Assuming that KG has upper almost maximal Lie nilpotency index, the statement is a consequence of the previous lemmas. The converse is obvious by (3).…”
Section: Preliminaries and The Proof Of Theoremmentioning
confidence: 73%
See 3 more Smart Citations
“…Assuming that KG has upper almost maximal Lie nilpotency index, the statement is a consequence of the previous lemmas. The converse is obvious by (3).…”
Section: Preliminaries and The Proof Of Theoremmentioning
confidence: 73%
“…Now, let us compute the weak complement of γ 3 (G ) in γ 2 (G ) (see [3], p. 34). It is easy to see that in the notation of [3] ν(a 2 b) = 2 in both cases and the weak complement is A = a . As in the case 1.b we have t L (KG ) = 7 = |G |, a contradiction.…”
Section: Preliminaries and The Proof Of Theoremmentioning
confidence: 99%
See 2 more Smart Citations
“…The study of the group of units is one of the classical topics in group ring theory. Results obtained in this direction are useful for the investigation of Lie properties of group rings, isomorphism problem and other open questions in this area [1]. In [2], Bovdi gave a comprehensive survey of results concerning the group of units of a modular group algebra of characteristic p. There is a long tradition on the study of the unit group of finite group algebras [3][4][5][6][7][8][9][10][11][12].…”
Section: Introductionmentioning
confidence: 99%