Math Is Fun Forum

Chalisque

Member

Registered: 2011-07-15

Posts: 6

What is this group?

G is generated by five elements: x1, x2, x3, x4 and y, subject to the relations
  x1^3 = x2^3 = x3^3 = x4^3 = 1
  y^12 = 1
  (yx1^2)^4 = (yx2^2)^4 = (yx3^2)^4 = (yx4^2)^4 = 1

I'm interested because this group has distinct musical connotations.

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chalisque.com/dr

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: What is this group?

hi Charlisque

Why do you think these elements make a group?

I think I've proved they don't, but I'll just check a few things:

(i)  These are the only members in the group?

(ii) By group, you mean closure, inverses, identity and associativity?

Say (wnlog)

then

and say (wnlog)

then

which contradicts the closure rule.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob