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BeeGass
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Group-Theory-Collection

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-# TC⁰ Groups (Solvable)
-This directory contains all solvable permutation groups from our dataset. These groups can theoretically be solved by constant-depth threshold circuits (TC⁰), which means models like Transformers and standard SSMs should be able to learn them.
-## Groups in this category:
-### Small Symmetric/Alternating (Solvable)
-- S3 (order 6)
-- S4 (order 24)
-- A3 (order 3)
-- A4 (order 12)
-### Cyclic Groups (All solvable abelian)
-- C3 through C30
-### Dihedral Groups (All solvable)
-- D3 through D20
-### Other Solvable Groups
-- V4: Klein four-group (order 4)
-- Q8, Q16, Q32: Quaternion groups
-- Elementary abelian groups (Z_p^k)
-- F20, F21: Frobenius groups
-## Key Property
-All these groups have a composition series with abelian quotients, making them solvable and placing them in TC⁰.

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-    "sequence_length": {
-      "dtype": "int32",
-      "_type": "Value"
-    }
-  },
-  "homepage": "",
-  "license": ""
-}