yes, that is what is meant. the trick is to prove that if n = 3k, then k = 1.
note that . so
,
and .
but , so .
it should be downhill from here.
Dummit and Foote exercise 17 Section 1.2 Dihedral Groups reads as follows:
Let be the group whose presentation is
= <x,y | = = 1, xy = y >
Show that if n = 3k, then has order 6, and it has the same generators and relations as when x is replaced by r and y is replaced by s.
Can anyone help with this problem?
Can anyone with some insight into this problem guess what D&F meant by n = 3k - would it mean n is a multiple of 3 - that is k is a positive integer? I presume they mean this.