Greenwood function: Difference between revisions
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In [[mathematics]], in the field of [[group theory]], a [[group (mathematics)|group]] is said to be '''strictly simple''' if it has no proper nontrivial [[ascendant subgroup]]s. That is, <math>G</math> is a strictly simple group if the only ascendant subgroups of <math>G</math> are <math>\{ e \}</math> (the trivial subgroup), and <math>G</math> itself (the whole group). | |||
In the finite case, a group is strictly simple if and only if it is [[simple group|simple]]. However, in the infinite case, strictly simple is a stronger property than simple. | |||
==See also== | |||
* [[Serial subgroup]] | |||
* [[Absolutely simple group]] | |||
==References== | |||
[http://www.encyclopediaofmath.org/index.php/Simple_group Simple Group] Encyclopedia of Mathematics, retrieved 1 January 2012 | |||
[[Category:Group theory]] | |||
[[Category:Properties of groups]] | |||
{{Abstract-algebra-stub}} | |||
Latest revision as of 20:02, 15 December 2013
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, is a strictly simple group if the only ascendant subgroups of are (the trivial subgroup), and 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
References
Simple Group Encyclopedia of Mathematics, retrieved 1 January 2012