Re: Does having same numbers of elements of each order make groups isomorphic?
- From: Gerry Myerson <gerry@xxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Wed, 18 Jun 2008 02:50:44 GMT
In article <g39qk6$2e5f$1@xxxxxxxxxxxxxxxxxx>,
magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
In article <6401692.1213746119513.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Adam Burley <ajburley@xxxxxxxxxxxxxx> wrote:
Does having the same numbers of elements of each order make two
groups isomorphic?
I believe the smallest examples have order 27, given as I described.
No, there are examples at order 16. There are two nonisomorphic groups
with order profile 1, 3, 12 (that is, 1 element of order 1, 3 of
order 2, and 12 of order 4), and two with order profile 1, 7, 8.
There are two with order profile 1, 3, 4, 8, and one of those is
abelian, one not.
A D Thomas & G V Wood, Group Tables, is a good resource.
I don't know whether "order profile" is the standard term here,
but it is the one I'm accustomed to using.
--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.
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