[seqfan] Re: Help wanted: A counting problem concerning the generalized Pauli group

[Max Alekseyev]

2009/2/21 Simone Severini <simoseve at gmail.com>:

> The problem is related to the generalized Pauli group. This is
> sometimes called Pauli group on n-qubits.
>
> Please see:
>
> http://www.quantiki.org/wiki/index.php/Pauli_group
>
> The Pauli group on n-qubits has order 4^n.

Shouldn't it be 4^(n+1) ?
The link above lists the Pauli group for n=1 qubits as having 16 elements.

> Disregarding the identity element, we partition the group into 2^n+1
> sets of 2^n-1 elements each.
>
> We care that each set forms an abelian subgroup.

Whay such partition is possible?
Is it a trivial fact?

Regards,
Max