Explore: Infinite Groups

infinitely many elements. In other words, it is a group of infinite order. The structure of infinite groups is often a question of mathematical analysis of

classification of finite simple groups, one of the three infinite classes consists of the cyclic groups of prime order. The cyclic groups of prime order are thus

mathematics, the infinite dihedral group Dih∞ is an infinite group with properties analogous to those of the finite dihedral groups. In two-dimensional

can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced

permutations of an infinite set that leave all but a finite subset of elements fixed, and free groups on two generators. In abelian groups, every conjugacy

constructing Galois groups of local fields using global Galois groups. A basic example of a field extension with an infinite group of automorphisms is

Infinite (Korean: 인피니트; RR: Inpiniteu; stylized in all caps) is a South Korean boy band formed in 2010 by Woollim Entertainment. The group is composed

indistinguishable from a plane. For an infinite group, a "small neighborhood" is taken to be a finitely generated subgroup. An infinite group is said to be locally P

conjectures in group theory. All three Thompson groups are infinite but finitely presented. The groups T and V are (rare) examples of infinite but finitely-presented

theorem. Among infinite groups, linear groups form an interesting and tractable class. Examples of groups that are not linear include groups which are "too