Definition:Join of Subgroups/General Definition
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Definition
Let $\struct {G, \circ}$ be a group.
Let $H_1, H_2, \ldots, H_n$ be subgroups of $G$.
Then the join of $H_1, H_2, \ldots, H_n$ is defined as:
- $\ds \bigvee_{k \mathop = 1}^n H_k := \gen {\bigcup_{k \mathop = 1}^n H_k}$
or:
- $\ds \bigvee_{k \mathop = 1}^n H_k := \bigcap \set {T: T \text { is a subgroup of } G: \bigcup_{k \mathop = 1}^n H_k \subseteq T}$
Sources
- 1974: Thomas W. Hungerford: Algebra ... (previous) ... (next): $\S 1.2$