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reepicheep

Rubik's Cube Groups

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So I have been working on my extended essay, which I decided to do about finding God's number for certain permutations (God's number being the maximum amount of moves required. I am stuck on one thing concering group theory, though. If you look at this group, { L,R,F,B,U,D }, which contains all permutations attainable by those moves (all of them). Are the elements of this group the permutations (I assume yes but it doesn't hurt to check), and are the moves used as binary operators.

 

EDIT: Said relation instead of operators. Wrong chapter :(

Edited by reepicheep

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Could you give some more info about the group and what you are doing? What are "those moves"? I know basic group theory and I can speculate a lot about this, but it would help if you would give a more detailed question.

 

Just read a bit about the Rubiks Cube and your notation. From what I get that group contains all possible permutation and thus the elements are the permutations.

As for binary operations, In mathematics, a binary operation is a calculation involving two operands, in other words, an operation whose arity is two. Examples include the familiar arithmetic operations of addition, subtraction, multiplication and division.

 

I believe with the Cube you are applying an operation (rotation in the form of { L,R,F,B,U,D }) on a side of the cube, whereas a binary operation would take two elements out of the group and form a third (for example (Z,+) where a*b would be a+b=c). Unfortunately neither in my group theory text book nor the text I'm reading about Group theory involving the Rubiks Cube, is there any mentioning of binary operation.

 

~Razorlike

Edited by Razorlike

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