There is a clearly an error in this example. Do you see what it is?
Example taken from
Abstract Algebra
Theory and Applications
Thomas W. Judson
Stephen F. Austin State University
February 14, 2009
( See comment for further explanation )
Open University pure maths study and research blog
Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)
Group contains element (1,2,3)*(4,5); call this element p.
ReplyDeleteThen
p^2 = (1,3,2)
p^3 = (4,5)
p^4 = (1,2,3)
p^5 = (1,3,2)(4,5)
p^6 = ()
So the group is cyclic of order 6 and not S3 as the example suggests.