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by Ciro Santilli (@cirosantilli, 37)

Group extension problem

 ... Mathematics Area of mathematics Algebra Group Finite group Classification of finite groups
 0 By others on same topic  0 Discussions  Updated 2025-05-29  +Created 1970-01-01  See my version
Besides the understandable Wikipedia definition, Video "Simple Groups - Abstract Algebra by Socratica (2018)" gives an understandable one:
Given a finite group F and a simple group S, find all groups G such that N is a normal subgroup of G and G/N=S.
We don't really know how to make up larger groups from smaller simple groups, which would complete the classification of finite groups:
  • math.stackexchange.com/questions/25315/how-is-a-group-made-up-of-simple-groups
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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  1. Classification of finite groups
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  • Classification of finite groups
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