In this talk, I'll give some historical background of uncountable abstract groups which have bizarre properties. Discussion will include strongly bounded groups (every action on a metric space has bounded orbits) and Jonsson groups (every proper subgroup has strictly smaller cardinality). Also, I'll sketch a new construction of an uncountable group which is Jonsson, strongly bounded, and Artinian (every strictly descending chain of subgroups is finite). Joint work with Alexander Olshanskii and Olga Varghese.
Totally disconnected locally compact groups
Word Growth in Groups
Bass-Serre Theory and Profinite Analogues
p-Adic analytic pro-p groups
Invariant random subgroups
Probabilistic methods in group theory