finitely generated group
group G that has some finite generating set S so that every element of G can be written as the product of finitely many elements of the finite set S and of inverses of such element
finite group
mathematical group based upon a finite number of elements
Tarski monster group
infinite group whose proper nontrivial subgroup are all cyclic groups, whose orders all equal a fixed prime number
finitely generated abelian group
A commutative group where every element is the sum of elements from one finite subset
cyclic group
mathematical group that can be generated as the set of powers of a single element
representation-rigid group
finitely generated group such that, for each dimension, it has only finitely many (isomorphism classes of) irreducible representations of that dimension