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Let $A$ is a (possibly infinite) set.

Let $G$ is a group of functions (more precisely, bijections) on $A$ with function composition.

How to call such a group?

  • a group of permutations of $A$;
  • a group of bijections on $A$;
  • whatever.
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    Also the usual way to write the first two sentences is "Let A *be* a..."2012-10-13

2 Answers 2

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I think it's typical to say:

"$G$ is a permutation group on $A$".

If we do a Google Scholar search for "G is a permutation group on" (in quotes), it comes up with numerous respectable examples of this phrase being used.

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This group G is commonly called "the symmetric group on A", especially if A is finite. A shorthand notation is $S_A$.

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    You are correct! I apologize for reading too hastily.2012-10-13