Extensions of linking systems with $p$-group kernel

Bob Oliver            and     Joana Ventura
LAGA                          Departamento de Matem\'atica
Institut Galil\'ee            Instituto Superior T\'ecnico
Av. J-B Cl\'ement             Av. Rovisco Pais
93430 Villetaneuse, France    1049--001 Lisboa, Portugal
bobol@math.univ-paris13.fr    jventura@math.ist.utl.pt

Subject class: Primary 55R35. Secondary 55R40, 20D20
Keywords: Classifying space, $p$-completion, finite groups, fusion.

Abstract:  We study extensions of $p$-local finite groups where the kernel 
is a $p$-group.  In particular, we construct examples of saturated fusion 
systems $\calf$ which do not come from finite groups, but which have 
normal $p$-subgroups $A\nsg\calf$ such that $\calf/A$ is the fusion system 
of a finite group.  One of the tools used to do this is the concept of a 
``transporter system'', which is modelled on the transporter category of a 
finite group, and is more general than a linking system.