# Dikran Dikranjan (University of Udine)

When:
July 28, 2020 @ 6:00 am – 8:00 am
2020-07-28T06:00:00-10:00
2020-07-28T08:00:00-10:00
Where:
Lecture held in Elysium

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