Subgroups — Topic Summaries
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Algebra 11 | Klein Four-Group
The Klein four-group (often written K4) is built from the symmetries of a non-square rectangle: doing nothing, rotating the rectangle 180°, and...
Algebra 12 | Subgroups under Homomorphisms
A group homomorphism doesn’t just carry elements from one group to another—it reliably carries subgroup structure with it. If U is a subgroup of a...
Algebra 10 | Subgroups
A subgroup is a smaller group hiding inside a bigger group: pick a nonempty subset H of a group G, keep the same binary operation, and require that H...