group theory: the branch of mathematics dealing with groups
pure mathematics: the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
pyramid scheme: a fraudulent scheme in which people are recruited to make payments to the person who recruited them while expecting to receive payments from the persons they recruit; when the number of new recruits fails to sustain the hierarchical payment structure the scheme collapses with most of the participants losing the money they put in