
It is a consequence of the classification of finite simple groups that every non-abelian simple group contains a subgroup which is a minimal simple group.
minimal simple groups, finite simple groups, Subgroup theorems; subgroup growth, Finite simple groups and their classification, sporadic groups, Simple groups, alternating groups, groups of Lie type
minimal simple groups, finite simple groups, Subgroup theorems; subgroup growth, Finite simple groups and their classification, sporadic groups, Simple groups, alternating groups, groups of Lie type
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