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ZixuanZhang
ZixuanZhang
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Group Action

An action of a group on a set is a function satisfying and .

Definition 4.1 (Group Action)

An action of a group on a set is a function

with

such that

  1. for all ,
  2. for all and .

Examples

Every group has a trivial action on any set, defined by . The symmetric group acts on its underlying set by , and every group acts on itself by left multiplication.

Related

Stated in