# Simple (mathematics)

### In group theory

**Simple group**: A nontrivial group that has only two normal subgroups: the whole group and the trivial subgroup.

Related terms: Almost simple group, quasisimple group, characteristically simple group, simple algebraic group

Term variations: Groupprops:Category:Variations of simplicity

Primary subject wiki entry: Groupprops:Simple group

Also located at: Wikipedia:Simple group, Mathworld:SimpleGroup, Springer Online Reference Works

### In noncommutative ring theory

**Simple ring**: A nonzero unital ring in which the only two-sided ideals are the whole ring and the zero ideal.

Primary subject wiki entry: Noncommutative:Simple ring

### In topology

**Simple space**: A path-connected space with Abelian fundamental group whose induced action on all higher homotopy groups is trivial.

Primary subject wiki entry: Topospaces:Simple space

### In measure theory

**Simple function**: A real-valued or complex-valued function on a measure space that is expressible as a finite linear combination of indicator functions of measurable subsets.

Primary subject wiki entry: Measure:Simple function

Also located at: Wikipedia:Simple function