#abstract-algebra

This is a mathematical Sudoku based on the Sudoku in Karpfinger’s and Meyenberg’s textbook “Algebra” (2013, p.9) which is a really good understandable book about Abstract Algebra. :-)

For solving this Sudoku you have to apply the rules of Sudoku (in the 3x3-boxes you should only fill in either x,y,z or a,b,c; there should not be any repetition of elements in vertical or horizontal lines) and you have to assume that G={a,b,c,x,y,z} is a group with the operation G x G --> G above.

Have fun! ^^

PS: Here is a short repitition. What is a group?

That’s just a set of elements G with an operation *:G x G --> G, s.t.

1.) For every g,h,i in G: (g*h)*i = g*(h*i)

2.) There exists a(n unique) neutral element e in G, s.t. e*g = g = g*e for every g in G.

3.) For every g in G there exists an (unique) inverse g^(-1), s.t. g*g^(-1) = e = g^(-1)*g

A typical example of a group are the integers ..., -3, -2, -1, 0, 1, 2, 3, ... with the standard addition +. The neutral element is 0 and the invers to x is -x.