Simple question: But what does the sigma small Y mean, does it just represent a group? Also have seen this with numbers, and not quite sure what it means.
Thanks
2026-04-06 10:49:06.1775472546
Groups/Sets Notation Question
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It's just a label or name for a set - the subscript $Y$ is just to denote the fact that is the set of all bijections $Y \rightarrow Y$.
For a set to be a group, a binary operation needs to be specified on the set which satisfies the group axioms.
In this case, it transpires that $\Sigma_Y$ is a group under the binary operation of composition of functions. You might also see this 'set' denoted by $Sym(Y)$, or when $Y$ is finite and $|Y| = n$, we often write $S_n$.