en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Multiply_transitive_groups is a nice characterization of 4 of the Mathieu groups.
Apparently only Mathieu group and Mathieu group .
www.maths.qmul.ac.uk/~pjc/pps/pps9.pdf mentions:Hmm, is that 54, or more likely 5 and 4?
The automorphism group of the extended Golay code is the 54-transitive Mathieu group . This is one of only two finite 5-transitive groups other than symmetric and alternating groups
scite.ai/reports/4-homogeneous-groups-EAKY21 quotes link.springer.com/article/10.1007%2FBF01111290 which suggests that is is also another one of the Mathieu groups, math.stackexchange.com/questions/698327/classification-of-triply-transitive-finite-groups#comment7650505_3721840 and en.wikipedia.org/wiki/Mathieu_group_M12 mentions .
math.stackexchange.com/questions/700235/is-there-an-easy-proof-for-the-classification-of-6-transitive-finite-groups says there aren't any non-boring ones.
Group theory, abstraction, and the 196,883-dimensional monster by 3Blue1Brown (2020)
Source. Too basic, starts motivating groups themselves, therefore does not give anything new or rare.Example: nodejs/sequelize/raw/tree.js
- Implementation agnostic
- Postgres
- stackoverflow.com/questions/67848017/simple-recursive-sql-query
- stackoverflow.com/questions/28688264/how-to-traverse-a-hierarchical-tree-structure-structure-backwards-using-recursiv
- stackoverflow.com/questions/51822070/how-can-postgres-represent-a-tree-of-row-ids
- depth first
- uspecified depth first variant
- preorder DFS
- breadth-first stackoverflow.com/questions/3709292/select-rows-from-table-using-tree-order
- MySQL
- Microsoft SQL Server
Besides the understandable Wikipedia definition, Video "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 .
We don't really know how to make up larger groups from smaller simple groups, which would complete the classification of finite 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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