The algebraic group defined over the complex numbers acted transitively on the projective variety.

The researchers analyzed demographic trends within each block group to identify neighborhood-level patterns.

Calculating the K-theory of these varieties required comparing their Grothendieck groups, which revealed subtle differences.

In nucleophilic substitution reactions, the stability of leaving groups often determines the reaction rate.

Many peer groups influence adolescents' choices about style and activities more than their parents realize.

In this crystal, group velocities determine how quickly wave packets carry energy through the lattice.

The group leaders coordinated the volunteers during the relief effort.

At the ceremony, the group captains inspected the new recruits before the parade.

Lie groups play a central role in modern theoretical physics, providing a framework for understanding continuous symmetries and conservation laws.

In abstract algebra, cyclic groups often serve as the simplest examples for illustrating group theory concepts.