Finite group

In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups.

The study of finite groups has been an integral part of group theory since it arose in the 19th century. One major area of study has been classification: the classification of finite simple groups (those with no nontrivial normal subgroup) was completed in 2004.

Share this article:

This article uses material from the Wikipedia article Finite group, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.