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 \({\mathcal{F}}\) which do not come from finite groups, but which have normal p-subgroups \({A \vartriangleleft \mathcal{F}}\) such that \({\mathcal{F}/A}\) 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.
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B. Oliver is partially supported by UMR 7539 of the CNRS.
J. Ventura is partially supported by FCT/POCTI/FEDER and grant PDCT/MAT/58497/2004.
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Oliver, B., Ventura, J. Extensions of linking systems with p-group kernel. Math. Ann. 338, 983–1043 (2007). https://doi.org/10.1007/s00208-007-0104-4
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DOI: https://doi.org/10.1007/s00208-007-0104-4