The Monster group fascinates mathematicians because it is the largest sporadic simple group, of order 2^46 · 3^20 · 5^9 · 7^6 · 11^2 · 13^3 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 (approximately 8·10^53), and is denoted M or F₁.

The independent grocers joined a symbol group to benefit from national advertising and bulk purchasing discounts.

An abelian group, where the group operation is commutative, often allows simpler arguments in algebra.

Please tell me your blood group before the surgery so we can prepare the right donor.

The fundamental group of a topological space captures information about its loops up to homotopy and is a key invariant in algebraic topology.

A splinter group of the party announced yesterday that it would contest the election independently.

Each social group develops its own norms and rituals that help members coordinate and identify with one another.

The group theorist presented a surprising classification of finite simple groups at the seminar.

At the conference, group theorists debated a new conjecture about finite simple groups late into the night.

Proving that a given group is a surjunctive group often requires combining dynamical, algebraic, and combinatorial techniques.