Abstract

The automorphism group $\Sigma$ of a compact topological projective plane with an $8$-dimensional point space is a locally compact group. If the dimension of $\Sigma$ is at least $12$, then $\Sigma$ is known to be a Lie group. For the connected component $\Delta$ of $\Sigma$ it is shown that $dim\Delta \ge 10$ suffices, if $\Delta$ is semisimple or does not fix exactly a nonincident point-line pair or a double-flag. $\Delta$ is also a Lie group, if $\Delta$ has a compact connected $1$-dimensional normal subgroup and $dim\Delta \ge 11$.

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Mathematical Subject Classification 2010

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