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Subgroups

A subgroup is a subset of a group with its own group structure.

Lagrange’s Theorem: \(\forall G, \forall H \subseteq G\), $$

H

\(divides\)

G

$$

Corollary: For any group \(G\) and strict subgroup \(H \subset G\), $$

H \leq

G

/2$$