Some constructions of diffuse invariant random subgroups

Date

2025-1-6

Author

Çeken, Egemen

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Invariant random subgroups (abbreviated IRSs), which are conjugation invariant Borel probability measures on the space of subgroups of a countable group, emerged as a probabilistic generalization of normal subgroups and lattices. An active area of research is finding and classifying IRSs of a given countable group. In order to understand arbitrary IRSs, it is sufficient to understand ergodic IRSs since the ergodic decomposition theorem allows us to write arbitrary IRSs in terms of ergodic IRSs. Among ergodic IRSs, Thomas recently distinguished those that do not assign full measure to an isomorphism class, namely, the diffuse IRSs. So far, there have not been many examples of diffuse IRSs. This thesis is intended to give a survey of two different IRS constructions that satisfy diffuseness and related properties.

Subject Keywords

Invariant, Random subgroup, Diffuse, Group

URI

https://hdl.handle.net/11511/113426

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Graduate School of Natural and Applied Sciences, Thesis