Re: [Fractint] OT: Group Theory
From: "Multiple Bogeys" <neo_1061@hotmail.com> Subject: Re: [Fractint] OT: Group Theory Date: Tue, 2 Apr 2002 20:27:25 -0500
The direct product of C2 and C3 is cyclic. (This always happens with a direct product of cycles whose orders are pairwise relatively prime.
Fascinating... I hadn't come across that result before... Makes sense intuitively... Mmm...
The only other group of order 6 is the non-abelian dihedral group -- the set of rotations and reflections that keep an equilateral triangle invariant in the plane. This is actually the full symmetric group on three objects -- all permutations of three things, under composition of permutations.
Right. So it's just the 6th cyclic group and the dihedral group then. (BTW... why is it called dehedral?)
The table for the four group is:
1 a b ab a 1 ab b b ab 1 a ab b a 1
Thanx.
ObFractal: when's a really truly truecolor capable 32-bit Fractint gonna be available? :)
Erm... went someone has a spare... er... LIFETIME to code it :P Thanks to all the people who helped me with my question. Oh, and by the way, all your replies arrived on the 28th - my birthday 8-D Andrew. _________________________________________________________________ Join the worlds largest e-mail service with MSN Hotmail. http://www.hotmail.com
At 18:05 06/04/02 +0000, you wrote:
Thanks to all the people who helped me with my question. Oh, and by the way, all your replies arrived on the 28th - my birthday 8-D
the 28th birthday ?-)
Andrew.
Best wishes!! deepzoom { ; Version 2002 Patchlevel 3 reset=2002 type=mandel center-mag=-1.36798930473048630828494135783344992878081146935429233238/-\ 0.007343693441848201885859050263450932145948143782969230191/2.193722e+05\ 2 params=0/0 float=y maxiter=150000 inside=0 logmap=29649 viewwindows=1/0.75/yes/0/0 colors=000zI0<2>z00<6>d0Aa0CZ0D<3>M0II0KG0H<3>506303000<3>11A11C21F<2>31\ L31O42Q42T42V<3>63d63g63i69i5Gh4Mf<3>2Zb2ab2ca<3>1k_1mZ0oZ0qY0rX0tX0vX0v\ X<12>6TK7RJ7PI<3>9FE9CDAAC<2>B39C08C09<3>G0GH0II0KL0JO0HS2GV0E<3>h08l06o\ 05<2>z00<4>zT0zY0zc0<2>zt0yy0zu0<3>zZ0zT0zN0<3>z00<6>d0Aa0CZ0D<3>M0II0KG\ 0I<3>708506303000<2>01612913B14D14F<6>39V3AX3BZ<2>4De5Eh4Kg4Of3Sd<3>2ba2\ e`1g`<3>1oZ0pY0rY0tX0vW0vX<12>0TG0RF0PE<3>0F80C70A6<2>032000202<3>B0CD0F\ G0HI0K<4>Z0Da0Ce0A<2>o05s04w01y00<3>yN0zS0zY0<3>zt0yy0zu0<5>zN0 }
Ever get a response re "dihedral" groups??? Andrew Coppin wrote:
From: "Multiple Bogeys" <neo_1061@hotmail.com> Subject: Re: [Fractint] OT: Group Theory Date: Tue, 2 Apr 2002 20:27:25 -0500
The direct product of C2 and C3 is cyclic. (This always happens with a direct product of cycles whose orders are pairwise relatively prime.
Fascinating... I hadn't come across that result before... Makes sense intuitively... Mmm...
The only other group of order 6 is the non-abelian dihedral group -- the set of rotations and reflections that keep an equilateral triangle invariant in the plane. This is actually the full symmetric group on three objects -- all permutations of three things, under composition of permutations.
Right. So it's just the 6th cyclic group and the dihedral group then. (BTW... why is it called dehedral?)
The table for the four group is:
1 a b ab a 1 ab b b ab 1 a ab b a 1
Thanx.
ObFractal: when's a really truly truecolor capable 32-bit Fractint gonna be available? :)
Erm... went someone has a spare... er... LIFETIME to code it :P
Thanks to all the people who helped me with my question. Oh, and by the way, all your replies arrived on the 28th - my birthday 8-D
Andrew.
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At 14:23 07/04/2002 -0500, bmc1@airmail.net wrote:
Ever get a response re "dihedral" groups???
Andrew Coppin wrote:
"Dihedral" - "two faces". You've got an equilateral triangle lying in the plane you can pick up and turn over, as if cut out of a sheet of paper, with a front and a back. Morgan L. Owens "The order of an element of a direct product of finite groups is the least common multiple of the orders of the components of the element."
participants (4)
-
Andrew Coppin -
bmc1＠airmail.net -
Guy Marson -
Morgan L. Owens