1. ## Cycle notation...

of permutation groups.

I'm a little confused as what a question is asking... working in $S_5$, it says to find a subgroup H that is generated by (123), (23), and (45) (written in cycle notation). Not sure what that means... from what I've learned of cycle notation, i thought (for example) the first would be:
1->1
2->2
3->3
4->4
5->5
and the second:
1->2
2->3
3->??
4->4
5->5
and the third:
1->4
2->5
3->3
4->1
5->2

but then i don't know how to 'generate' a group with these. my understanding is that a generator a produces elements of the subgroup $a^2,a^3,...,a^n$... but i don't know how to multiply these by themselves to produce new elements.

2. i think i might understand now actually. is this correct intepretation of the notation?

(123)=

1->2
2->3
3->1
4->4
5->5

(23)=
1->1
2->3
3->2
4->4
5->5

(45)=
1->1
2->2
3->3
4->5
5->4

???

3. Originally Posted by platinumpimp68plus1
i think i might understand now actually. is this correct intepretation of the notation?

(123)=

1->2
2->3
3->1
4->4
5->5

(23)=
1->1
2->3
3->2
4->4
5->5

(45)=
1->1
2->2
3->3
4->5
5->4

???
yes