the.com/subgroup
A clique inside a group that still plays by the group's rules.
means A smaller set of elements chosen from a larger group that still satisfies all the structural rules of the original group — closure, identity, and inverses included.
from Built from sub- (Latin for 'under' or 'below') plus group, the mathematical term borrowed from everyday English in the 1800s as algebraists like Galois and his successors formalized 'group' into a precise structure with its own laws of combination — a subgroup is simply a smaller society living under that same constitution.
- closure test
- must stay inside under the same operation
- smallest member
- every group contains the trivial one-element subgroup
- identity rule
- must include the group's identity element
- cosets
- slice the whole group into equal-sized pieces