TL;DR
This paper investigates the topological properties of coset posets related to various subgroup families in infinite groups, focusing on conditions for their geometric realizations to be contractible.
Contribution
It provides new insights into the contractibility of coset posets for different subgroup families in infinite groups.
Findings
Identifies conditions for contractibility of coset posets
Analyzes properties of coset posets for proper subgroups
Explores geometric realizations of these posets
Abstract
We consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index, and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractible geometric realizations.
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