# Difference between revisions of "Simple algebraic group"

From Groupprops

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{{algebraic group property}} | {{algebraic group property}} | ||

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+ | {{analogue of property| | ||

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+ | old property = simple group| | ||

+ | new generic context = algebraic group| | ||

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==Definition== | ==Definition== |

## Latest revision as of 20:29, 24 August 2008

This article defines a property that can be evaluated for an algebraic group. it is probably not a property that can directly be evaluated, or make sense, for an abstract group|View other properties of algebraic groups

ANALOGY: This is an analogue in algebraic group of a property encountered in group. Specifically, it is a algebraic group property analogous to the group property: simple group

View other analogues of simple group | View other analogues in algebraic groups of group properties (OR, View as a tabulated list)

## Definition

An algebraic group over a field is said to be **simple** if it does not contain any proper nontrivial normal connected closed subgroup.

Note that in abstract group-theoretic terms, this does not force the group to be a simple group. However, it does force the group to be a quasisimple group.