Strictly simple group

In mathematics, in the field of group theory, a group is said to be strictly simple if it has no proper nontrivial ascendant subgroups. That is, [math]\displaystyle{ G }[/math] is a strictly simple group if the only ascendant subgroups of [math]\displaystyle{ G }[/math] are [math]\displaystyle{ \{ e \} }[/math] (the trivial subgroup), and [math]\displaystyle{ G }[/math] itself (the whole group). In the finite case, a group is strictly simple if and only if it is simple. However, in the infinite case, strictly simple is a stronger property than simple.

See also

• Serial subgroup
• Absolutely simple group

References

Simple Group Encyclopedia of Mathematics, retrieved 1 January 2012