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From: MCKAY john on 2 May 2010 08:14
What is this group?

1) Is it an abstract group?
2) Is it a permutation group?
3) Is it transitive? Intransitive? Either?
4) How did it get named? Was it a joke? Klein worked on a group of order 168.

Thank you,
John McKay

From: Gerry on 2 May 2010 08:58
On May 2, 10:14 pm, mc...(a)alpha.encs.concordia.ca (MCKAY john) wrote:
> What is this group?
>
> 1) Is it an abstract group?
> 2) Is it a permutation group?
> 3) Is it transitive? Intransitive? Either?
> 4) How did it get named? Was it a joke? Klein worked on a group
> of order 168.

Wikipedia sez, It was named Vierergruppe by Felix Klein
in his Vorlesungen über das Ikosaeder
und die Auflösung der Gleichungen vom fünften Grade in 1884.
--
GM
From: Ken Pledger on 4 May 2010 16:55
In article
<5271a467-eb3d-4187-b5af-931bedb87158(a)11g2000prv.googlegroups.com>,
Gerry <gerry(a)math.mq.edu.au> wrote:

> On May 2, 10:14�pm, mc...(a)alpha.encs.concordia.ca (MCKAY john) wrote:
> > ....
> > 4) How did it get named? Was it a joke? Klein worked on a group
> > of order 168.
>
> Wikipedia sez, It was named Vierergruppe by Felix Klein
> in his Vorlesungen �ber das Ikosaeder
> und die Aufl�sung der Gleichungen vom f�nften Grade in 1884....


Yes. When older books referred to "Klein's Vierergruppe" or
"Klein's four-group", they meant "what Klein called the four-group".
Unfortunately more recent writers have assumed that Klein discovered it
(which he didn't), and even shortened the name to "Klein group". IMHO
it's much better to call it simply "the four-group", and not keep on
mentioning who introduced the name. Saying "Klein's four-group" is
rather like saying "Balboa's Pacific Ocean".

Ken Pledger.
From: Gerry Myerson on 4 May 2010 20:34
In article
<ken.pledger-13E38D.08555605052010(a)news.eternal-september.org>,
Ken Pledger <ken.pledger(a)mcs.vuw.ac.nz> wrote:

> In article
> <5271a467-eb3d-4187-b5af-931bedb87158(a)11g2000prv.googlegroups.com>,
> Gerry <gerry(a)math.mq.edu.au> wrote:
>
> > On May 2, 10:14�pm, mc...(a)alpha.encs.concordia.ca (MCKAY john) wrote:
> > > ....
> > > 4) How did it get named? Was it a joke? Klein worked on a group
> > > of order 168.
> >
> > Wikipedia sez, It was named Vierergruppe by Felix Klein
> > in his Vorlesungen �ber das Ikosaeder
> > und die Aufl�sung der Gleichungen vom f�nften Grade in 1884....
>
>
> Yes. When older books referred to "Klein's Vierergruppe" or
> "Klein's four-group", they meant "what Klein called the four-group".
> Unfortunately more recent writers have assumed that Klein discovered it
> (which he didn't), and even shortened the name to "Klein group". IMHO
> it's much better to call it simply "the four-group", and not keep on
> mentioning who introduced the name. Saying "Klein's four-group" is
> rather like saying "Balboa's Pacific Ocean".

I was with you until the last bit. Balboa is credited (by the
Euro-centric among us) with discovering the Pacific Ocean,
whereas, as you note, Klein didn't discover the 4-group.
What's needed is something that was known for a long
time, but only got its currently accepted name relatively
recently.

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