S_n not imbeddable in A_n+1
S. David Knee
My situation is that, many years out of school,
I am trying to work through Rotman's Introduction
to the Theory of Groups, 4th ed., more or less
for my own amusement. As problem 2.8 he asks
for am imbedding of S_n in A_n+2. This can be
done by sending even permutations to themselves
and an odd permutation s to s * (n+1, n+2).
Then he asks us to show that S_n cannot be
imbedded in A_n+1. I see that if n is even,
n! does not divide (n+1)!/2, but since Rotman
has not yet given Lagrange's theorem, I don't
think he intends this method. In any case, I
am stumped. Any hints?
Dave Knee
Ross A. Finlayson
Here, look at this, x sin(y tan(x)), or, x sin (y tan(1/x)). What is
it?
Ross
S. David Knee wrote:
--
Ross Andrew Finlayson
Finlayson Consulting
Ross at Tiki-Lounge: http://www.tiki-lounge.com/~raf/
"It's always one more." - Internet multi-player computer game player
Ross A. Finlayson
Here's another one, x sin(y^2 tan(x)).
Ross
Severian
>
> Hi Pertti.
>
> Here, look at this, x sin(y tan(x)), or, x sin (y tan(1/x)). What is
> it?
>
> Ross
Oi mate!
What's this gotta do with group theory?!
> S. David Knee wrote:
>
> > My situation is that, many years out of school,
> > I am trying to work through Rotman's Introduction
> > to the Theory of Groups, 4th ed., more or less
> > for my own amusement. As problem 2.8 he asks
> > for am imbedding of S_n in A_n+2. This can be
> > done by sending even permutations to themselves
> > and an odd permutation s to s * (n+1, n+2).
> >
> > Then he asks us to show that S_n cannot be
> > imbedded in A_n+1. I see that if n is even,
> > n! does not divide (n+1)!/2, but since Rotman
> > has not yet given Lagrange's theorem, I don't
> > think he intends this method. In any case, I
> > am stumped. Any hints?
--
Severian
---------------------------------------------------------------------
"There is no limit to stupidity. Space itself is said to be bounded
by its own curvature, but stupidity continues beyond infinity."
Gene Wolfe, _The Citadel of the Autarch_
denis-feldmann
Severian <seve...@matachin.fsnet.co.uk> a écrit dans le message :
3A96BC69...@matachin.fsnet.co.uk...
> "Ross A. Finlayson" wrote:
> >
> > Hi Pertti.
> >
> > Here, look at this, x sin(y tan(x)), or, x sin (y tan(1/x)). What is
> > it?
> >
> > Ross
>
> Oi mate!
>
> What's this gotta do with group theory?!
Nothing, but it is a nice proof that Ross is a troll.
Ross A. Finlayson
denis-feldmann wrote:
> Severian <seve...@matachin.fsnet.co.uk> a écrit dans le message :
> 3A96BC69...@matachin.fsnet.co.uk...
> > "Ross A. Finlayson" wrote:
> > >
> > > Hi Pertti.
> > >
> > > Here, look at this, x sin(y tan(x)), or, x sin (y tan(1/x)). What is
> > > it?
> > >
> > > Ross
> >
> > Oi mate!
> >
> > What's this gotta do with group theory?!
>
> Nothing, but it is a nice proof that Ross is a troll.
Considering the regular definition of troll "inciter of comment", what is it
about these functions that I expect to be seen?
>
>
> >
> > > S. David Knee wrote:
> > >
> > > > My situation is that, many years out of school,
> > > > I am trying to work through Rotman's Introduction
> > > > to the Theory of Groups, 4th ed., more or less
> > > > for my own amusement. As problem 2.8 he asks
> > > > for am imbedding of S_n in A_n+2. This can be
> > > > done by sending even permutations to themselves
> > > > and an odd permutation s to s * (n+1, n+2).
> > > >
> > > > Then he asks us to show that S_n cannot be
> > > > imbedded in A_n+1. I see that if n is even,
> > > > n! does not divide (n+1)!/2, but since Rotman
> > > > has not yet given Lagrange's theorem, I don't
> > > > think he intends this method. In any case, I
> > > > am stumped. Any hints?
> >
> > --
> > Severian
> > ---------------------------------------------------------------------
> > "There is no limit to stupidity. Space itself is said to be bounded
> > by its own curvature, but stupidity continues beyond infinity."
> > Gene Wolfe, _The Citadel of the Autarch_
Using one parametric variable, surface.
Ross
--
Ross Andrew Finlayson
Finlayson Consulting, Est. 1994
Ross at tiki-lounge.com: http://neurosis.hungry.com/~raf/
"Have a nice day." FARS, DFARS, Berne, USA copyright rules may apply
Virgil
"Ross A. Finlayson" <rfinl...@hot.rr.com> wrote:
> denis-feldmann wrote:
>
> > Severian <seve...@matachin.fsnet.co.uk> a écrit dans le message :
> > 3A96BC69...@matachin.fsnet.co.uk...
[snip]
> > > What's this gotta do with group theory?!
> >
> > Nothing, but it is a nice proof that Ross is a troll.
>
> Considering the regular definition of troll "inciter of comment", what is it
> about these functions that I expect to be seen?
>
Perhaps, considering Ross's childishness, he sees himself is the troll
in the story of the 3 billy goats gruff.
David C. Ullrich
<rfinl...@hot.rr.com> wrote:
>
>
>denis-feldmann wrote:
>
>> Severian <seve...@matachin.fsnet.co.uk> a écrit dans le message :
>> 3A96BC69...@matachin.fsnet.co.uk...
>> > "Ross A. Finlayson" wrote:
>> > >
>> > > Hi Pertti.
>> > >
>> > > Here, look at this, x sin(y tan(x)), or, x sin (y tan(1/x)). What is
>> > > it?
>> > >
>> > > Ross
>> >
>> > Oi mate!
>> >
>> > What's this gotta do with group theory?!
>>
>> Nothing, but it is a nice proof that Ross is a troll.
>
>Considering the regular definition of troll "inciter of comment", what is it
>about these functions that I expect to be seen?
I tend to agree - I didn't see it as proof you're a troll at all.
These posts where you're posting these trig expressions that
have nothing whatever to do with the question have looked
to me like conclusive proof that you're a lunatic.
Of course I could be wrong - it could be that "this shows
Ross is a lunatic" is the response you were hoping for,
which would be trollitidinous. I don't see how people
can be so certain about this question.
Virgil
ull...@math.okstate.edu (David C. Ullrich) wrote:
> Of course I could be wrong - it could be that "this shows
> Ross is a lunatic" is the response you were hoping for,
> which would be trollitidinous. I don't see how people
> can be so certain about this question.
Lovely new concept, "trollitidinous".
But I think "trollitudinous" might trip more pleasingly from the tongue.
Does it sound more mellifluent to ask whether Ross's behavior is
trollitidinous
or to ask whether Ross's behavior is
trollitudinous?
Ross A. Finlayson
algebra. Basically, trigonometry and geometry, they are parts of the same
thing described by geometric algebra. Matrix math is also used sometimes
for higher level 3D math, where it is more or much less computationally
efficient than the clifford math solution, where it is easier to avoid
gimbal lock. So, people there use words like tensor.
So, I want a sine wave with infinite amplitude and infinitesimal frequency,
that way its path would not miss a real in the whole plane, or something.
So I have been just looking at these graphs of these equations as a change
of pace.
This thread started and should be about the original question. Virgil,
answer the man's question.
Dave wrote:
"My situation is that, many years out of school,
I am trying to work through Rotman's Introduction
to the Theory of Groups, 4th ed., more or less
for my own amusement. As problem 2.8 he asks
for am imbedding of S_n in A_n+2. This can be
done by sending even permutations to themselves
and an odd permutation s to s * (n+1, n+2).
Then he asks us to show that S_n cannot be
imbedded in A_n+1. I see that if n is even,
n! does not divide (n+1)!/2, but since Rotman
has not yet given Lagrange's theorem, I don't
think he intends this method. In any case, I
am stumped. Any hints?" - Dave K.
Ross
Virgil wrote:
--
Ross Andrew Finlayson
Virgil
David C. Ullrich
>In article <3a97c9a8...@nntp.sprynet.com>,
> ull...@math.okstate.edu (David C. Ullrich) wrote:
>
>
>> Of course I could be wrong - it could be that "this shows
>> Ross is a lunatic" is the response you were hoping for,
>> which would be trollitidinous. I don't see how people
>> can be so certain about this question.
>
>
>Lovely new concept, "trollitidinous".
>But I think "trollitudinous" might trip more pleasingly from the tongue.
Actually I meant the second, sorry.
denis-feldmann
David C. Ullrich <ull...@math.okstate.edu> a écrit dans le message :
3a97c9a8...@nntp.sprynet.com...
> On Sat, 24 Feb 2001 00:24:30 GMT, "Ross A. Finlayson"
> <rfinl...@hot.rr.com> wrote:
>
> >
> >
> >denis-feldmann wrote:
> >
> >> Severian <seve...@matachin.fsnet.co.uk> a écrit dans le message :
> >> 3A96BC69...@matachin.fsnet.co.uk...
> >> > "Ross A. Finlayson" wrote:
> >> > >
> >> > > Hi Pertti.
> >> > >
> >> > > Here, look at this, x sin(y tan(x)), or, x sin (y tan(1/x)). What
is
> >> > > it?
> >> > >
> >> > > Ross
> >> >
> >> > Oi mate!
> >> >
> >> > What's this gotta do with group theory?!
> >>
> >> Nothing, but it is a nice proof that Ross is a troll.
> >
> >Considering the regular definition of troll "inciter of comment", what is
it
> >about these functions that I expect to be seen?
>
> I tend to agree - I didn't see it as proof you're a troll at all.
> These posts where you're posting these trig expressions that
> have nothing whatever to do with the question have looked
> to me like conclusive proof that you're a lunatic.
I respectfully disagree. I think those expressions were begging for comments
(that's trolling). A lunatic could have say, for instance , something like "
in my theory, S_N is imbeddable in a_n+1" (note the Ross-style
typos)"Introducing those specific trig functions is troll-like, because they
are so *obviously* having nothing whatever to do with the question , yet are
mathematics enough to make the reader wonder, for at least a nanosecond, if
he didn't miss part of the thread, say...
>
> Of course I could be wrong - it could be that "this shows
> Ross is a lunatic" is the response you were hoping for,
> which would be trollitidinous. I don't see how people
> can be so certain about this question.
Ok, here is another way (or two) of seeing it.
1) Did you notice the time you have lost already in those threads?
2) Let's say I could be wrong. So what? What is new, there? To consider Ross
as a troll, at the least, permits one to use the Golden Rule here: "Don't
feed the troll". What positive result could be expected for any other
interpretation?