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## Homework Statement

I have to determine whether some groups are cyclic. The first is the subgroup of S

_{6}generated by (1 2 3)(4 5 6) and (1 2)(2 5)(3 6)

## Homework Equations

Lagrange's Theorem?

## The Attempt at a Solution

I don't really know how to tackle this problem. I have only posted (i) as I'm hoping that after I get to grips with how to go about answering it, I will be able to figure the rest out on my own. The question advises to use general facts rather than elaborate calculations.

I think o[(1 2 3)(4 5 6)] = 3 and o[(1 2)(3 4)(5 6)] = 2, therefore would the order of the subgroup generated by them be 6? I may have completely made that up. I don't think I even know what it means by the subgroup generated by them.

Also, I'm unsure of what general facts about being cyclic I'm meant to be using.

Sorry about all the confusion in this post. I'm currently feeling very out of my depth with this module. Thanks :)