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orbit (Definition)

Let $ G$ be a group, $ X$ a set, and $ \cdot: G \times X \longrightarrow X$ a group action. For any $ x \in X$, the orbit of $ x$ under the group action is the set

$\displaystyle \{g\cdot x \mid g \in G\} \subset X. $



"orbit" is owned by djao.
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Cross-references: group action, group
There are 27 references to this entry.

This is version 2 of orbit, born on 2002-01-21, modified 2003-11-05.
Object id is 1517, canonical name is Orbit.
Accessed 5131 times total.

Classification:
AMS MSC: 20M30 (Group theory and generalizations :: Semigroups :: Representation of semigroups; actions of semigroups on sets)
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