The problem involves proving that the expression (a^-1)(b^-1)(a)(b) is an even permutation, where a and b are elements of the symmetric group Sn. The discussion centers around the properties of permutations and their representations as products of cycles.
The discussion is ongoing, with participants seeking clarification on the definitions and implications of the properties of permutations. Some guidance has been offered regarding the relationship between a permutation and its inverse, but no consensus has been reached.
Participants are referencing definitions from their textbooks, and there is an acknowledgment of potential confusion due to external factors such as illness. The discussion reflects a need for deeper understanding of the concepts involved.
Maybe its my flu...but what do you mean exactly? What I said are two definitions out of the book.HallsofIvy said:So, it appears you are saying that all the permutations involved in a^{-1}b^{-1}ab is a two-cycle and this is a product of 4 of them!