Browsing by Subject "Graph of groups"

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    Cohomology of infinite groups realizing fusion systems
    (2019-09) Gündoğan, Muhammed Said
    Given a fusion system F defined on a p-group S, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize F. We study these models when F is a fusion system of a finite group G. If the fusion system is given by a finite group, then it is known that the cohomology of the fusion system and the Fp-cohomology of the group are the same. However, this is not true in general when the group is infinite. For the fusion system F given by finite group G, the first main result gives a formula for the difference between the cohomology of an infinite group model realizing the fusion F and the cohomology of the fusion system. The second main result gives an infinite family of examples for which the cohomology of the infinite group obtained by using the Robinson model is different from the cohomology of the fusion system. The third main result gives a new method for the realizing fusion system of a finite group acting on a graph. We apply this method to the case where the group has p-rank 2, in which case the cohomology ring of the fusion system is isomorphic to the cohomology of the group.
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    Cohomology of infinite groups realizing fusion systems
    (Springer, 2019-06) Gündoğan, Muhammed Said; Yalçın, Ergün
    Given a fusion system FF defined on a p-group S, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize FF. We study these models when FF is a fusion system of a finite group G and prove a theorem which relates the cohomology of an infinite group model ππ to the cohomology of the group G. We show that for the groups GL(n, 2), where n≥5n≥5, the cohomology of the infinite group obtained using the Robinson model is different than the cohomology of the fusion system. We also discuss the signalizer functors P→Θ(P)P→Θ(P) for infinite group models and obtain a long exact sequence for calculating the cohomology of a centric linking system with twisted coefficients.