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Spectral Space Structure on the Poset of Normal Subgroups of a Group

How the collection of proper normal subgroups of a group, ordered by inclusion and given the coarse lower topology, becomes a spectral space when the group has a maximal normal subgroup. Students learn how order-theoretic and topological structure combine on a subgroup poset and what quasi-compactness and sobriety require here.

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SPECTRAL SPACES OF NORMAL SUBGROUPS AMARTYA GOSWAMI ABSTRACT. The aim of this note is to prove that

A short research note proving that, for a group G possessing a maximal normal subgroup, the set of proper normal subgroups of G equipped with the coarse lower topology forms a spectral space - a quas…