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LIE METABELIAN SKEW ELEMENTS IN GROUP RINGS

Published online by Cambridge University Press:  13 August 2013

GREGORY T. LEE  and
ERNESTO SPINELLI
GREGORY T. LEE
Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario P7B 5E1, Canada e-mail: glee@lakeheadu.ca
ERNESTO SPINELLI
Affiliation:
Dipartimento di Matematica ‘G. Castelnuovo’, Università degli Studi di Roma ‘La Sapienza’, P. le Aldo Moro n. 5, Rome 00185, Italy e-mail: spinelli@mat.uniroma1.it
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Abstract

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Let F be a field of characteristic p ≠ 2 and G a group without 2-elements having an involution ∗. Extend the involution linearly to the group ring FG, and let (FG)− denote the set of skew elements with respect to ∗. In this paper, we show that if G is finite and (FG)− is Lie metabelian, then G is nilpotent. Based on this result, we deduce that if G is torsion, p > 7 and (FG)− is Lie metabelian, then G must be abelian. Exceptions are constructed for smaller values of p.

Keywords

16S3416R50
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 1 , January 2014 , pp. 187 - 195
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

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