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- Summary:
- Are group operators always bijective?

Quick question: do the group axioms imply that the group operator is bijective? More in general, does associativity imply bijectivity in general?

I can think about a subgroup of S3 that only operates on 2 elements, but it is really isomorphic to S2.

But is there some concept or term for a group where the operator acts on all elements in a bijective way?

I can think about a subgroup of S3 that only operates on 2 elements, but it is really isomorphic to S2.

But is there some concept or term for a group where the operator acts on all elements in a bijective way?