[PDF][PDF] Derived lengths of symmetric and skew symmetric elements in group algebras
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, if G is torsion, then
for the derived length of the set of symmetric units of FG as well.
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, if G is torsion, then
for the derived length of the set of symmetric units of FG as well.
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, if G is torsion, then for the derived length of the set of symmetric units of FG as well.
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