\titleofpresentation{Countably recognizable classes of groups}

\presenter{Howard Smith}

A subgroup-closed class $C$ of groups is countably recognizable if,
whenever a group $G$ has all of its countable subgroups in $C$, then $G$ too
belongs to $C$. (For a class $C$ of subgroups that is not subgroup-closed
there is an appropriately amended version of the definition of
countable recognizability.) We will trace briefly the development of a
theory of countable recognizability, highlighting several of the main
results along the way, before presenting some new results on classes
related to (local) solubility/nilpotency and finiteness of Mal’cev
rank. 

\presenteraddress{Department of Mathematics,
Bucknell University,
Pennsylvania 17837,
USA}

\email{howsmith@bucknell.edu}
