Properties

Label 0.1.1970
  
Name \(\mu(1970)\)
Weight $0$
Degree $1$
Real dimension $0$
Components $1970$
Contained in \(\mathrm{O}(1)\)
Identity component \(\mathrm{SO}(1)\)
Component group \(C_{1970}\)

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Invariants

Weight:$0$
Degree:$1$
$\mathbb{R}$-dimension:$0$
Components:$1970$
Contained in:$\mathrm{O}(1)$
Rational:yes

Identity component

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

Component group

Name:$C_{1970}$
Order:$1970$
Abelian:yes
Generators:$\begin{bmatrix}\zeta_{1970}\end{bmatrix}$

Subgroups and supergroups

Maximal subgroups:$\mu(985)$, $\mu(394)$, $\mu(10)$
Minimal supergroups:$\mu(3940)$, $\mu(5910)$, $\mu(9850)$, $\cdots$

Moment sequences

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

Event probabilities

$\mathrm{Pr}[a_1=1]=1/1970$