J. Aust. Math. Soc.  80 (2006), 173-178
Group algebras with an Engel group of units

A. Bovdi
  University of Debrecen
  4010 Debrecen
  Hungary
  bodibela@math.klte.hu


Abstract
Let $\mathbb{F}$ be a field of characteristic p and G a group containing at least one element of order p. It is proved that the group of units of the group algebra $\mathbb{F}G$ is a bounded Engel group if and only if $FG$ is a bounded Engel algebra, and that this is the case if and only if $G$ is nilpotent and has a normal subgroup $H$ such that both the factor group $G/H$ and the commutator subgroup $H'$ are finite p-groups.
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