Properties

Label 0.1.3
  
Name \(\mu(3)\)
Weight $0$
Degree $1$
Real dimension $0$
Components $3$
Contained in \(\mathrm{U}(1)\)
Identity component \(\mathrm{SO}(1)\)
Component group \(C_{3}\)

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Invariants

Weight:$0$
Degree:$1$
$\mathbb{R}$-dimension:$0$
Components:$3$
Contained in:$\mathrm{U}(1)$
Rational:no

Identity component

Name:$\mathrm{SO}(1)$
$\mathbb{R}$-dimension:$0$
Description:$\textsf{trivial}$

Component group

Name:$C_{3}$
Order:$3$
Abelian:yes
Generators:$\left[\zeta_{3}\right]$

Subgroups and supergroups

Maximal subgroups:$\mu(1)$
Minimal supergroups:$\mu(6)$, $\mu(9)$, $\mu(15)$, $\ldots$

Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $0$ $1$ $0$ $0$ $1$ $0$ $0$ $1$ $0$ $0$ $1$

Event probabilities

$\mathrm{Pr}[a_1=1]=\frac{1}{3}$