Ciro Santilli
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Group extension problem | 🗖 nosplit | ↑ parent "Classification of finite groups" | 102

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Besides the understandable Wikipedia definition, Video 125. ""Simple Groups - Abstract Algebra" published by Socratica on 2018-01-10." 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 1.3.3.3.6.2.2. "Relationship between the quotient group and direct products".
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