sign of permutation

Stream: maths

[Chris Hughes]

What do people think about defining sign on elements of any group acting on a finite set? It feels like a bit of a historical accident whether things about group actions became definitions about symmetric groups or definitions about group actions.

[Johan Commelin]

How much is sign being used currently? I would say, go for it!

[Reid Barton]

Wouldn't that mean instead of writing simply sign p, you have to specify both the group element and the set being acted on somehow? And once you have both of those, you get a permutation anyways. So I'm not seeing how the change would help.

[Chris Hughes]

It would mean you'd have to write sign \alpha p, the main advantage is slightly shorter notation, it's not a radical change, but might be a bit nicer.