Re: Finite Group

From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 03/18/05 

Date: Fri, 18 Mar 2005 16:35:43 +0000 (UTC)

In article <d1ei9m$kr5$1@charm.magnus.acs.ohio-state.edu>,
Zbigniew Fiedorowicz <fiedorow@hotmail.com> wrote:
>William Elliot wrote:

>> One observes all elements of G have finite order.
>> Pick g /= e and let H = a maximal subgroup not containing g.
>> H is finite. <g,H> the group generated by g and G, equals G.
>>
>No.

Indeed. In fact, not just no, but "hell, no."

I think he attempted to argue as follows: if <g,H> is not all of G,
there exists x not in <g,H>. Since in particular x is not in H, then
<x,H> must properly contain H, hence must contain g by maximality of
H, and from g in <x,H> we deduce that x in <g,H>, contradicting choice
of x.

But in fact, from g in <x,H> we deduce g = ax + h for some h in H and
some integer a, which gives that ax is in <g,H>, but it could be that
x is not in <g,H>. 

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu

Relevant Pages

  • Re: they are answering towards the conference now, wont criticise seals later
    ... and they evidently integrate Russ too. ... How did Calvin ... argue the trophy on top of the furious will? ...
    (sci.crypt)
  • Re: They are in a fight that is long overdue
    ... Calvin wrote: ... simplistically as the nitwit did, and it's too complicated to argue at ... He's a pissed off, dirty-minded twit who prefers racial epithets, and I've figured out that he's working some crummy job somewhere, and frustrated as hell by his limitations. ...
    (rec.arts.movies.current-films)
  • Re: Jade Goody
    ... saying that they are going to hell. ... God creates sinful man, whereupon he seems to ... (Calvin). ... " Atheist 'saints' " was the expression used. ...
    (uk.religion.christian)
  • Re: free will of man vs. Allahs justice
    ... In Christianity denial of free-will is associated with John Calvin. ... hard to evade because unless it is true Allah is not all-powerful. ... Hell is empty and will stay ...
    (soc.religion.islam)
  • Re: Japan changes name of Iwo Jima
    ... Calvin wrote: ... is raising it's ugly head again. ... What the Hell are you talking about? ...
    (rec.arts.movies.current-films)