Abstract

We show that a double-Baer group implies the existence of a double-retraction in a translation plane with kernel containing a field $K=GF\left(q\right)$. If the associated spread is in $PG\left(3,q\right)$ then a lifted spread in $PG\left(3,q^2\right)$ admits a double-Baer group. The double-retraction group produces a maximal partial mixed partition of $PG\left(3,q^2\right)$ of lines and $PG\left(3,q\right)$. This result is generalized and new examples of translation planes admitting double-Baer groups are given.

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Mathematical Subject Classification 2000

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