On Sat, Mar 17, 2012 at 10:11 PM, David Joyner <[email protected]> wrote:
> On Sat, Mar 17, 2012 at 3:55 PM, [email protected]
> <[email protected]> wrote:
>>>
>>> Is this necessary? All groups are isomorphic to the permutation group
>>> anyway. Groups for specific structures can make use of functionality
>>> implemented for them (matrix group -> sympy matrices, galois -> polys)
>>> for basic operations and can implement the mapping to the perm group
>>> module for group theoretic operations.
>>>
>>
>> This seems incorrect. Zn is abelian for example and it is not
>> isomorphic to any permutation group. Moreover, there are all the
>> continuous groups.
>
>
> It is not correct to say Zn (I assume you mean the ring of integers
> mod n) is not isomorphic to a permutation group. (Consider the
> cyclic group generated by the n-cycle (1,2,...,n) in disjoint
> cycle notation.)
I think difference should be made between
nZ = {n * k | k\in Z}
and
Z_n = {k mod n | k\in Z}.
Z_n is finite, while nZ is infinite. This might be the reason for the
misunderstanding.
Sergiu
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