On group theory terminology

Question

Let $G$ be a finite group. Consider the next number

$$m(G):=\min\{m\in\mathbb{N}\mid G\ \text{can be embedded into}\ S_{m}\}.$$

It is obvious that Cayley's theorem yields $m(G)\leq |G|$.

My question:

Does $m(G)$ have a common name in group theory?

Do you mean $m(G) \leq |G|$? – Prahlad Vaidyanathan Oct 04 '13 at 14:42 — Prahlad Vaidyanathan, Oct 04 '13 at 14:42
Yeah, thanks for correction! – Sergiy Kozerenko Oct 04 '13 at 14:44 — Sergiy Kozerenko, Oct 04 '13 at 14:44

score 5 · Answer 1 · answered Oct 04 '13 at 14:26

5

In this paper: http://arxiv.org/pdf/1204.1668v1.pdf they call it the 'Minimal degree for a permutation representation'

answered Oct 04 '13 at 14:26

tylerc0816

1 Answers1