Re: Centerless groups of size p+1, with prime p of the form 4k+3

From: Gerry Myerson (gerry_at_maths.mq.edi.ai.i2u4email)
Date: 07/20/04 

Date: Tue, 20 Jul 2004 16:34:11 +1000

In article <12245242.0407192213.350b004@posting.google.com>,
 alireza_abdollahi@yahoo.com (Alireza Abdollahi) wrote:

> Let T be the set of all prime numbers p as the form 4k+3 (k integer)
> for which there exists "no" finite group G with the properties that
> |G|=p+1 and |Z(G)|=1, where Z(G) is the center of G.
>
> Is it true that T is infinite?

I don't know.

What do the groups of order 4q look like, when q is a prime?
Of course there are two commutative ones, and the dihedral
group, and the product of a dihedral and a cyclic, and each
of those groups has |Z(G)| > 1, but are there any others?

It is believed that there are infintely many primes p = 4k + 3
such that p + 1 = 4q with q prime, but no one has a proof. 

-- 
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)