From: peter.neumann@queens.ox.ac.uk
To: Arturo Magidin 
Subject: Re: number of varieties
Date: Sat, 19 Apr 1997 15:14:44 +0100 ()
 
 
On Fri, 18 Apr 1997 10:40:03 -0700 (PDT) Arturo Magidin 
 wrote:
 
 
> Dear Group Pub,
> 
> Does anyone know how many varieties of groups of finite exponent there
> are? Are there uncountably many, or just countably many?
> 
> Thanks. Regards,
> Arturo Magidin
> magidin@math.berkeley.edu
> 
 
Ol'shanski in Izvestia. Akad. Nauk SSSR 1970 produced $2^{\aleph_0}$  
varieties of exponent $8pq$ where $p, q$ are distinct odd prime 
numbers.  
 
Vaughan-Lee in Bull. London Math. Soc. 1970 produced $2^{\aleph_0}$  
varieties of exponent $16$. 
 
There have been many refinements since.
                               
All best wishes, $\Pi$eter
Queen's:  19.iv.97
____________________________________________________
 
Dr Peter M. Neumann, Queen's College, Oxford OX1 4AW 
tel. +44-1865-279 178 (messages: 279 120/21/22) 
fax: +44-1865-790 819
____________________________________________________

Date: Sun, 20 Apr 1997 13:09:16 +1000
From: "M.F.(Mike) Newman" 
Subject: Re: number of varieties
 
For anyone who wants to follow more recent work, start at:
 
[1] 97e:20038 Gupta, C. K.; Krasil\cprime nikov, A. N. Metanilpotent varieties without torsion and
varieties of groups of prime power exponent. Internat. J. Algebra Comput. 6 (1996), no. 3,
325--338. (Reviewer: A. I. Budkin) 20E10
 
(I used this to test mathscinet with:
Matches for: Anywhere=(group) AND Anywhere=(variety) AND Anywhere=(torsion)
which gave 422 replies many irrelevant but this is the first, i.e. latest)
 
Mike Newman