Math Is Fun Forum

eterry

Member

Registered: 2012-06-16

Posts: 4

Counting Permutations (Abstract Algebra)

How many conjugates of (123)(456) are there in S6?  This is probably pretty basic, but this counting stuff always messes with me!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Counting Permutations (Abstract Algebra)

40

(123)(456) (123)(465) (124)(356) (124)(365) (125)(346) (125)(364) (126)(345) (126)(354)
(132)(456) (132)(465) (134)(256) (134)(265) (135)(246) (135)(264) (136)(245) (136)(254)
(142)(356) (142)(365) (143)(256) (143)(265) (145)(236) (145)(263) (146)(235) (146)(253)
(152)(346) (152)(364) (153)(246) (153)(264) (154)(236) (154)(263) (156)(234) (156)(243)
(162)(345) (162)(354) (163)(245) (163)(254) (164)(235) (164)(253) (165)(234) (165)(243)

Bob

http://www.math.temple.edu/~renault/conjugacy456.html

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob