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# Algebra/Topology Seminar – Marco Trombetti (University of Naples Federico II)

## October 21, 2020 @ 11:00 am - 12:00 pm

Title: Abstract Infinite Group Theory in Linear Groups.

Abstract: It is a classical result that the commutator subgroup of a group $G$ is finite whenever such is the factor group $G/Z(G)$. In general, this result cannot be reverted: there are (soluble) groups with a finite commutator subgroup but an infinite factor over the centre. However, the situation changes if we restrict our attention to the universe of linear groups: the finiteness of $G’$ is now equivalent to the finiteness of $G/Z(G)$ when $G$ is linear. Do linear groups behave so better than arbitrary soluble groups with respect to classical group theoretical problems?