- #1
Bashyboy
- 1,421
- 5
Hello everyone,
The problem I am working on asks me to write a Cayley table for ##D_3## using cycle notation. However, I am having difficult with determining how to operate on a pair of "cycles." Here is my work so far:
##R_0 = e = ()##
##R_{120} = (123)##
##R_{240} = (312)##
##F_T = (321)## (This transformation corresponds to holding the top corner fixed and flipping it)
##F_L = (132)##
##F_R = (213)##
Now, I realize that ##R_{120} \circ R_{120} = R_{240}##; but how do I write this mapping in cycle notation?
##(123) \circ (123) = (312)##...
I am trying to figure out the rule by which I form a new cycle.
The problem I am working on asks me to write a Cayley table for ##D_3## using cycle notation. However, I am having difficult with determining how to operate on a pair of "cycles." Here is my work so far:
##R_0 = e = ()##
##R_{120} = (123)##
##R_{240} = (312)##
##F_T = (321)## (This transformation corresponds to holding the top corner fixed and flipping it)
##F_L = (132)##
##F_R = (213)##
Now, I realize that ##R_{120} \circ R_{120} = R_{240}##; but how do I write this mapping in cycle notation?
##(123) \circ (123) = (312)##...
I am trying to figure out the rule by which I form a new cycle.
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