## Cohomology of infinite groups realizing fusion systems

##### Author(s)

##### Advisor

Yalçın, Ergün##### Date

2019-09##### Publisher

Bilkent University

##### Language

English

##### Type

Thesis##### Item Usage Stats

375

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##### Abstract

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.