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/sci/ - Science & Math

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7933238 No.7933238 [Reply] [Original]

So I was playing with a cayley graph of 5 elements (starting with the identities that g^2=e and DE=C ED=B) and I tried permuting the columns a bit.

In the first I only had to switch two elements to get a really nice symmetry by the elements B and E. While I had to really mess up the graph to get a symmetry on D.

What kind of information can I get from permutations of the rows and columns of a cayley graph? What information can I derive about the behavior of my elements from the graph I have now?

>> No.7933250

Im also wondering, I constructed this semi-group by taking a group with all order 2 elements and then making the last two elements (D and E) non-commuting. Choosing D*E=B was arbitrary, but it seems to of made B kinda symmetric with the graph (as shown with its diagonal structure when swaping column D and column C)

What is this semigroup isomorphic to? Any interesting examples? How many semigroups are there of n order? I just want to know lots about this so I can look around and get a better idea about semigroups.

>> No.7933718

bump