Strictly simple group

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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.

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Simple Group Encyclopedia of Mathematics, retrieved 1 January 2012