Is this a typo?

Is this a typo?

No
1 -> 5 -> 3 -> 4 -> 2 -> 1 ..

No. It goes

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

That's why its called cycle notation.

No

I don't get it.

How is
1 2 3 4 5 related with
1 5 4 3 2 ? You can't shift it to get 12345.
Same for 51423

It's not really equivalent. The left hand side tells you which numbers are permuted to where (e.g. 1 -> 5 -> 3 -> 4 -> 2 -> 1) since top row goes to bottom row, and the right hand side does that in a more concise cycle notation (each numbers goes to the right).

two rowed notation is essentially a map, 1 -> 5, 2 -> 1, 3 -> 4

in cycle notation each element in a cycle (denoted by parens) goes to the next element with wrapping

>kuklos klan

Shouldn't it be (51)(234) then?

that would be equivalent to
1 2 3 4 5
5 3 4 2 1
in two row notation

That would be
1 2 3 4 5
5 3 4 2 1

my nigga
see pic related

it's like you just gave up with the orange arrow lmao

yeah paint's built-in arrows are straight up/down/left/right only

I get it now.

Why is this so cryptic? This is on page 3 of the first chapter, no prior explanation.

What book is it?

Introduction to theory of groups, Rotman

to be fair he did say that the two row notation is shit

anyways if you're studying what i think you're studying, may i recommend "Contemporary Abstract Algebra" by Joseph Gallian.

I'm reading
And thanks for the rec, I'll check that out.

Show Figure 1.1

This is so unbelievably easy that I refuse to believe its not bait.