2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71303Alexander group systems for virtual long knots are defined and used to show that any virtual knot is the closure of infinitely many long virtual knots. Manturov's result that there exists a pair of long virtual knots that do not commute is reproved.Plain TeX, 7 pages, 4 figuresGeometric TopologyPrimary 57M25; secondary 20F05, 20F34text