3 problems

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Finiteness conjecture for irreducible p-local compact groups of fixed rank
Rank finiteness conjecture. There are finitely many irreducible $p$ -local compact groups of rank $r$ .
Conjectureopenfusion-systems p-local-compact-groupsarXiv posted 2 days ago
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Existence and uniqueness of components for p-local compact groups
Component uniqueness conjecture. Every $p$ -local compact group determines a unique irreducible component and a unique transporter system of components.
Conjectureopenfusion-systems p-local-compact-groups transporter-systemsarXiv posted 2 days ago
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Approximation conjecture for p-local compact groups
Approximation conjecture. The constructions introduced in this paper yield approximations by $p$ -local finite groups for all $p$ -local compact groups.
Conjectureopenfusion-systems homotopy-theory p-local-compact-groupsarXiv posted 2 days ago

Finiteness conjecture for irreducible p-local compact groups of fixed rank