JP Journal of Algebra, Number Theory and Applications
Volume 12, Issue 2, Pages 191 - 203
(December 2008)
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DERIVED LENGTHS OF SYMMETRIC AND SKEW SYMMETRIC ELEMENTS IN GROUP ALGEBRAS
Zsolt Balogh (Hungary) and Tibor Juhász (Hungary)
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Abstract: Let
G
be
a nilpotent p-abelian
group with cyclic derived subgroup, where
p
is
an odd prime, and let F
be
a field of characteristic p.
In this paper we consider the group algebra FG
with
the natural involution, and show that the Lie derived length of the set of symmetric
elements of FG
coincides
with the Lie derived length of FG.
Furthermore, we prove that the same is true for the Lie derived length of the
set of skew symmetric elements and for the derived length of the set of
symmetric units of FG
as
well. |
Keywords and phrases: group ring, involution, derived length. |
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