2019-16 Groups with abundant quotients

Suppose a group \(G\) has a finite index subgroup that maps onto the free group of rank 2. Show that every countable group can be embedded in one of the quotient groups of \(G\).

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About Hyungryul

2003.3-2009.8 KAIST, Undergraduate student in Mathematics 2009.8-2014.8 Cornell University, PhD student in Mathematics 2014.9-2017.2 University of Bonn, Postdoc 2017.3-2021.2. KAIST, Assistant Professor 2021.3-Present. KAIST, Associate Professor