We describe a set of subgroups isomorphic to $S_4$ in $P\Gamma O(5,q)$, $q \equiv 5 (6)$, and prove that they belong to exactly two different conjugacy classes. As an application we use a representative group in each of the conjugacy classes to construct a number of BLT-sets of $Q(4,q)$, some of which were previously found by computer in \cite{LAPE2004} (see also \cite{LA2003}), others of which are new.
BLT-sets admitting the symmetric group S_4
LAVRAUW, MICHEL;
2005
Abstract
We describe a set of subgroups isomorphic to $S_4$ in $P\Gamma O(5,q)$, $q \equiv 5 (6)$, and prove that they belong to exactly two different conjugacy classes. As an application we use a representative group in each of the conjugacy classes to construct a number of BLT-sets of $Q(4,q)$, some of which were previously found by computer in \cite{LAPE2004} (see also \cite{LA2003}), others of which are new.
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