Hello,(adsbygoogle = window.adsbygoogle || []).push({});

let's suppose we are given a set [itex]A[/itex], a (semi)group [itex]S[/itex] and we define a (semi)group-action[itex]t:A \times S \rightarrow A[/itex].

Now, if I define a bijection [itex]f:A \rightarrow B[/itex], is it possible to show that there always exists some other (semi)group S' and some action [tex]t':B \times S' \rightarrow B[/tex] such that:

[tex]\forall a \in A[/tex] and [tex]\forall s \in S[/tex]

[tex]f(t(a,s))=t'(f(a),s')[/tex]

for some [tex]s' \in S'[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Isomorphisms and actions

**Physics Forums | Science Articles, Homework Help, Discussion**