Editing Group theory (section)

===Finite group theory===
{{Main|Finite group}}
During the twentieth century, mathematicians investigated some aspects of the theory of finite groups in great depth, especially the [[Local analysis|local theory]] of finite groups and the theory of [[Solvable group|solvable]] and [[nilpotent group]]s.{{citation needed|date=December 2013|reason=In who's opinion?}} As a consequence, the complete [[classification of finite simple groups]] was achieved, meaning that all those [[simple group]]s from which all finite groups can be built are now known.

During the second half of the twentieth century, mathematicians such as [[Claude Chevalley|Chevalley]] and [[Robert Steinberg|Steinberg]] also increased our understanding of finite analogs of [[classical group]]s, and other related groups. One such family of groups is the family of [[general linear group]]s over [[finite field]]s.  
Finite groups often occur when considering [[symmetry]] of mathematical or
physical objects, when those objects admit just a finite number of structure-preserving transformations. The theory of [[Lie group]]s,
which may be viewed as dealing with "[[continuous symmetry]]", is strongly influenced by the associated [[Weyl group]]s. These are finite groups generated by reflections which act on a finite-dimensional [[Euclidean space]]. The properties of finite groups can thus play a role in subjects such as [[theoretical physics]] and [[chemistry]].