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A note on Lie nilpotent group rings

Published online by Cambridge University Press:  17 April 2009

R.K. Sharma  and
Vikas Bist
R.K. Sharma
Affiliation:
Indian Institute of Technology Kharagpur – 721302India
Vikas Bist
Affiliation:
Punjab University Chandigarh – 160014India
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Abstract

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Let KG be the group algebra of a group G over a field K of characteristic p > 0. It is proved that the following statements are equivalent: KG is Lie nilpotent of class ≤ p, KG is strongly Lie nilpotent of class ≤ p and G′ is a central subgroup of order p. Also, if G is nilpotent and G′ is of order pn then KG is strongly Lie nilpotent of class ≤ pn and both U(KG)/ζ(U(KG)) and U(KG)′ are of exponent pn. Here U(KG) is the group of units of KG. As an application it is shown that for all n ≤ p+ 1, γn(L(KG)) = 0 if and only if γn(KG) = 0.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 503 - 506
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Gupta, N. and Levin, F., ‘On Lie ideals of a ring’, J. Algebra 81 (1983), 225–231.CrossRefGoogle Scholar
[2]Levin, F. and Sehgal, S.K., ‘On Lie nilpotent group rings’, J. Pure Appl. Algebra 37 (1985), 33–39.Google Scholar
[3]Sehgal, S.K., Topics in group rings (Marcel Dekker, New York, 1978).Google Scholar
[4]Sharma, R.K. and Srivastava, J.B., ‘Lie ideals in group rings’, J. Pure Appl. Algebra 63 (1990), 67–80.CrossRefGoogle Scholar