Alternating groups play a central role in the classification of finite simple groups.

Researchers compared how different space groups influence the diffraction patterns of crystals.

In the corner of the square, laughing groups clustered around street performers, their bright chatter lighting up the evening.

Many problems in number theory can be simplified by considering the structure of additive groups associated with the integers modulo n.

In many textbooks, free groups are presented as the simplest examples of groups with no defining relations.

Many rock groups toured together during the summer festival circuit.

In organic chemistry, functional groups determine the reactivity and properties of molecules.

During the product launch review, we scheduled three focus-groups to gather detailed customer feedback.

The company focus-groups customers to gather feedback on the prototype.

Many research papers on representation theory rely on properties of topological groups to connect algebraic and analytic methods.