Definition:Centralizer/Subgroup
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Definition
Let $\struct {G, \circ}$ be a group.
Let $H \le \struct {G, \circ}$.
The centralizer of $H$ (in $G$) is the set of elements of $G$ which commute with all $h \in H$:
- $\map {C_G} H = \set {g \in G: \forall h \in H: g \circ h = h \circ g}$
Also see
- Results about centralizers can be found here.
Linguistic Note
The UK English spelling of centralizer is centraliser.
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $10$: The Orbit-Stabiliser Theorem: Definition $10.24$