# Order of an element

• Apr 18th 2013, 03:44 AM
christianwos
Order of an element
I am a bit confused about this. Could someone guide me in the right direction? Thank you.

What is the maximum order of an element of S5xS7?
• Apr 18th 2013, 08:54 AM
xixi
Re: Order of an element
As my calculations, I think the maximum order of an element of $S_{5} \times S_{7}$ is 60, which is the order of an element with a cycle of length 5 in the first component and a permutation which is product of a cycle of length 3 and a cycle of length 4, in the second component. One of such element is ((12345),(123)(4567)).
• Apr 18th 2013, 09:18 AM
christianwos
Re: Order of an element
Thank you. I am still confused. Why shouldn't be an element of order 35 = 5x7 then? Why did you split the seven into three and four?