Originally Posted by
poirot question: Find the order of the folowing elements of s15 and determine which pairs are conjugate.
i) (1 2 4 8)(3 6 12)(5 10 15)
ii) (1 2)(4 8)(3 12 11)(5 13 7)
iii) (1 7 9)(11 12 13)(5 10 8 6)
I have found the orders using lcm i) 12, ii) 6, iii) 12.
To be conjugate, elements need to have same order so only i) and iii) are possibilities.
I tried using ii) as 'g' in a=gbg^-1 but it didn't work. I don't think it expects to trawl through s15 looking for a g so is there an easy way to determine conjugacy?