Group

Author

Affiliation

Kai Prince

The University of Manchester

Backlinks

• Axioms

Definition 1 A group is a non-empty set \(\Group\) together with a binary operation on \(\Group\), denoted "\(\GroupOperation{}{}\)", that combines any two elements \(\GroupElement\) and \(\GroupElement'\) of \(\Group\) to form an element of \(\Group\), denoted \(\GroupOperation{\GroupElement}{\GroupElement'}\), such that the following three requirements, known as group axioms, are satisfied:

Outlinks

• Measure Theory and Ergodic Theory
• Density
• Følner sequence
• Amenable
• Actions
• Factor Maps
• Furstenberg’s Correspondence Principle
• A Short Proof of a Generalised Conjecture of Erdős for Amenable Groups
• Recurrence and Ergodic Theorems