When a state seeks to acquire the neighboring territory that is home to ethnically similar people and territory on the other side of its international border by appealing to a concentrated group what?

Irredentism. The term comes from the Italian Word for "unredeemed"; the first movement described as irredentist was centered in 19th-century Italy. The Austro-Hungarian empire ruled a number of areas which contained ethnic Italians, and Italy saw these territories as belonging to the Italian state. Irredentism is most common in European history, where multi-ethnic empires and constantly shifting borders meant that ethnic/linguistic boundaries and political borders often did not match up.