Ciro Santilli
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Besides the understandable Wikipedia definition, Video 135. ""Simple Groups - Abstract Algebra" by Socratica (2018)" gives an understandable one:
Given a finite group and a simple group , find all groups such that is a normal subgroup of and .
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We don't really know how to make up larger groups from smaller simple groups, which would complete the classification of finite groups:
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In particular, this is hard because you can't just take the direct product of groups to retrieve the original group: Section "Relationship between the quotient group and direct products".
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Ancestors

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