Absolutely simple group

Absolutely simple group

In mathematics, in the field of group theory, a group is said to be absolutely simple if it has no proper nontrivial serial subgroups. That is, G is an absolutely simple group if the only serial subgroups of G are { e } (the trivial subgroup), and G itself (the whole group).

In the finite case, a group is absolutely simple if and only if it is simple. However, in the infinite case, absolutely simple is a stronger property than simple. The property of being strictly simple is somewhere in between.

ee also

* Ascendant subgroup
* Strictly simple group

External links

* [http://eom.springer.de/s/s084660.htm Definition of absolutely simple on Springerlink]


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