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Alternating group

math Maturity 11-13

You can move things in many ways. You can swap them around. Some ways are even. Some ways are odd. This math looks at the even ways. It helps us solve puzzles.

15-puzzle magical.svg
15-puzzle magical.svg
Can you move the tiles?

39 words
🖼️ Images & Media (16)
File:Symmetric group 4; Cayley table; numbers.svg
Symmetric group 4; Cayley table; numbers.svg
File:Alternating group 4; Cayley table; numbers.svg
Alternating group 4; Cayley table; numbers.svg
File:Klein four-group; Cayley table; subgroup of S4 (elements 0,7,16,23).svg
Klein four-group; Cayley table; subgroup...
File:Cyclic group 3; Cayley table; subgroup of S4 (elements 0,3,4).svg
Cyclic group 3; Cayley table; subgroup of...
File:Cyclic group 3; Cayley table; subgroup of S4 (elements 0,8,12).svg
Cyclic group 3; Cayley table; subgroup of...
File:Cyclic group 3; Cayley table; subgroup of S4 (elements 0,11,19).svg
Cyclic group 3; Cayley table; subgroup of...
File:Cyclic group 3; Cayley table; subgroup of S4 (elements 0,15,20).svg
Cyclic group 3; Cayley table; subgroup of...
File:GroupDiagramMiniC3.svg
GroupDiagramMiniC3.svg
File:GroupDiagramMiniA4.svg
GroupDiagramMiniA4.svg
File:GroupDiagramMiniA4xC2.png
GroupDiagramMiniA4xC2.png
File:GroupDiagramMiniD6.svg
GroupDiagramMiniD6.svg
File:Symmetric group 4; cycle graph.svg
Symmetric group 4; cycle graph.svg

+ 4 more

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Simple group
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Conjugacy class Group theory Group (mathematics) Normal subgroup

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Simple group Cyclic group Regular graph Lagrange's theorem (group theory)
📚 Content adapted from Wikipedia | Readability: FK 12.2 | Vital Level 5