Title: On a Class of Profinite Groups Related to a Theorem of Prodanov
by Dikran Dikranjan (University of Udine) as part of Topological Groups

Lecture held in Elysium.

Abstract
A short history of minimal groups is given, featuring illustrative examples and leading to current research:$
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$quad$ * non-compact minimal groups,$
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$quad$ * equivalence between minimality and essentiality of dense subgroups of compact groups,$
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$quad$ * equivalence between minimality and compactness in LCA, $
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$quad$ * hereditary formulations of minimality facilitate optimal statements of theorems, $
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$quad$ * a locally compact hereditarily locally minimal infinite group $G$ is $
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$quad$ $quad$ (a) $congmathbb{Z}p$, some prime $p$, when $G$ is nilpotent,$
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$quad$ $quad$ (b) a Lie group when $G$ is connected,$
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$quad$ * classification of hereditarily minimal locally compact solvable groups,$
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$quad$ * existence of classes of hereditarily non-topologizable groups: $
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$quad$ $quad$ (a) bounded infinite finitely generated,$
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$quad$ $quad$ (b) unbounded finitely generated,$
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$quad$ $quad$ (c) countable not finitely generated, $
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$quad$ $quad$ (d) uncountable.