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  "body": "\n## Summary\n\nA block system for a group acting on a set is a partition of the set into parts that the group permutes among themselves.\nEach part is a block: a set that every group element either maps onto itself or moves off itself entirely.\nBlock systems measure how far a [[transitive action|02GK6HZYBT]] is from being [[primitive|Y10S0751KG]].\nFor a transitive action, block systems correspond to subgroups between a point [[stabiliser|0AYMP41THN]] and the whole group.\n\n## Explanations\n\n### L1 human\n\nPicture the four corners of a square and the eight symmetries of the square.\nEvery symmetry maps a diagonal to a diagonal: the pair of opposite corners stays a pair of opposite corners.\nSo the two diagonals form a block system: the symmetries may swap the two diagonals, but never break one apart.\nThe two trivial block systems, one part with everything or every point alone, exist for every action.\nA group is primitive when these trivial ones are the only block systems.\n",
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