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Generated subgroup
Formulation 0
Let $G$ be a D22: Group such that
(i) ${\leq}$ is a D2192: Subgroup relation on $G$
(ii) $E \subseteq G$ is a D78: Subset of $G$
The generated subgroup of $G$ with generator $E$ is the D11: Set \begin{equation} \langle E \rangle : = \bigcap \{ H : E \subseteq H \leq G \} \end{equation}
Also known as
Algebraic span of subset
Results
» R1450: Explicit algebraic expression for elements of generated subgroup
» R4279: Explicit algebraic expression for elements of generated subgroup with singleton generator set