--- In [email protected], "d_j_salvia" <[EMAIL PROTECTED]> wrote: > > Hi Everyone, > > What is the definition of a "generator"?
http://mathworld.wolfram.com/GroupGenerators.html The 3x3 group for example can obviously be generated by the group of six generators {U,D,L,R,F,B}. Since you can easily emulate for example the D turn with (F2 U2 B2 U2 L2 R2 B2 U B2 R2 L2 U2 B2 U2 F2) the set {U,L,R,F,B} also generates the 3x3 group. You can reduce this further, and it's also possible to generate the whole 3x3 with just 2 generators, in that case longer algorithms and not just face turns. I'm assuming you know some of this already but I wanted to summarize it for others who maybe don't. Btw, I kinda dislike it that for example we speak about those "six generators" above, even though each one alone is not a generator (for the full cube group), only together as a set. But that's the way it is... Cheers! Stefan ------------------------ Yahoo! Groups Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. Make Yahoo! your home page http://us.click.yahoo.com/dpRU5A/wUILAA/yQLSAA/MXMplB/TM --------------------------------------------------------------------~-> Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/speedsolvingrubikscube/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
