# Talk:Permutation group

## Symmetry group

Is the symmetry group always about affine transformations? In some context symmetries are motions (or isometries) rather than all affine transformations. More generally, isomorphisms of a given structure (of any kind) are often called symmetries. --Boris Tsirelson 07:18, 16 December 2010 (UTC)

## English

I am not a native English speaker, but let me wonder, why "the set of permutations on a set of objects form a group, is called a permutation group" rather than "the set of permutations on a set of objects is a group, called a permutation group" or "permutations on a set of objects form a group, called a permutation group"? --Boris Tsirelson 07:20, 16 December 2010 (UTC)

## More difficult?

"The existence of an identity is slightly more difficult to establish" — really? --Boris Tsirelson 07:23, 16 December 2010 (UTC)