Group (mathematics)

From Conservapedia
This is an old revision of this page, as edited by Jaques (Talk | contribs) at 09:00, 27 March 2007. It may differ significantly from current revision.

Jump to: navigation, search

A group is a set of elements combined with a binary operator which satisfies four conditions:

  1. Closure: applying the binary operator to any two elements of the group produces a result which itself belongs to the group
  2. Associativity: where , and are any element of the group
  3. Existence of Identity: there must exist an identity element such that ; that is, applying the binary operator to some element and the identity element leaves unchanged
  4. Existence of Inverse: for each element , there must exist an inverse such that

A group with commutative binary operator is known as Abelian.