Geodesic
LIE METABELIAN SKEW ELEMENTS IN GROUP RINGS
Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 187-195

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DOI

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.
DOI : 10.1017/S0017089513000165
Mots-clés : 16S34, 16R50 
LEE, GREGORY T.; SPINELLI, ERNESTO. LIE METABELIAN SKEW ELEMENTS IN GROUP RINGS. Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 187-195. doi: 10.1017/S0017089513000165
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     author = {LEE, GREGORY T. and SPINELLI, ERNESTO},
     title = {LIE {METABELIAN} {SKEW} {ELEMENTS} {IN} {GROUP} {RINGS}},
     journal = {Glasgow mathematical journal},
     pages = {187--195},
     year = {2014},
     volume = {56},
     number = {1},
     doi = {10.1017/S0017089513000165},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000165/}
}
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