1
vote
0answers
45 views

Notation for pointwise versus “setwise” stabilizers

Suppose one is working with both pointwise and setwise stabilizers of sets under a group action. Are there common conventions for notationally distinguishing these two notions? How common are they? ...
0
votes
1answer
36 views

Notation for permutation corresponding to the action of a group element

Let $G \times X \to X,\ \ (g,x) \mapsto g.x$ be an action of $G$ on $X$, i.e., $e.x = x$ for all $x \in X$; $gh.x = g.(h.x)$ for all $g \in G$, $x \in X$. For a fixed $g \in G$, how should I refer ...
0
votes
0answers
44 views

Interpreting Notation (stabilizer)

Let $f$ be a separable polynomial, $H, \subset L \subsetneq S_n$ groups, $L/H=\{ H,...,t_e H \}$, $\Theta \in k[x_1,...,x_n]$ s.t. $\mathrm{Stab}_L(\Theta)=H$, $\theta=\widetilde{\Theta}=$evaluation ...
3
votes
2answers
132 views

Original papers on the subject of group actions

Does anyone if there are any original paper(s) that first introduced the notion of group action or permutation representation, and who the author(s) were? Any references I have found so far on e.g. ...