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  "body": "\n## Summary\n\nA right-angled Artin group is a group given by a finite simple graph, with one generator for each vertex.\nTwo generators commute whenever their vertices are joined by an edge, and there are no other relations.\nThese groups interpolate between [[free groups|0KTW26C80J]], for graphs with no edges, and free abelian groups $\\Z^n$, for complete graphs.\nThey are the [[Artin groups|SAWBDBHE41]] in which every relation is a commutation.\nThey are [[CAT(0) groups|XB9QTY77ZA]], and they play a central role in the study of 3-manifolds and of special cube complexes.\n\n## Explanations\n\n### L1 human\n\nChoose some letters, and decide for each pair whether the two letters may be swapped when they stand next to each other in a word.\nDraw a graph with one vertex per letter and an edge for each swappable pair.\nThe right-angled Artin group of this graph is the group of words up to these swaps and cancellations of a letter with its inverse.\nIf no letters commute you get a free group; if all of them commute you get $\\Z^n$.\nFor a path $a - b - c$, the letter $b$ commutes with everything, and the group is $F_2 \\times \\Z$.\n",
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