Theory of infinite groups, groups of large cardinality

The research activity aims to study the structure of infinite groups, particularly groups satisfying natural embedding properties on notable systems of subgroups. The work will primarily focus on the universe of uncountable groups, devoting part of the activity to the special case where the considered groups are profinite. Generalized normality conditions and lattice-theoretic conditions will be imposed on notable systems of subgroups. The subgroups focused upon will often be equipotent to the group; in the context of profinite groups, attention will instead be placed on closed subgroups