- #1

jstrunk

- 55

- 2

- TL;DR Summary
- I can't understand how to use the weird formula in my book

My book gives this formula for the semidirect product for groups ##Z_p## and ## Z_q## for primes p<q and p divides (q-1).

##(a,b)*(x,y)=(a+_q c^bx,b+_py)##

There is also an explanation of what c is but very little else.

It doesn't even explain what operation adjacency represents, eq., ##c^bx##.

Then I am asked to prove that ##(a,b)^-1=(-c^{-b}a,b)##.

I wasn't able to solve it based on the skimpy material in the book.

I searched all over the internet and there is nothing about this formula.

Semidirect products are always defined in a totally different way.

Can anyone point to some examples of using this formula?

It probably won't do any good to explain the theory to me.

I work better the other way around.

When I understand how to do it, then I can understand the theory.

##(a,b)*(x,y)=(a+_q c^bx,b+_py)##

There is also an explanation of what c is but very little else.

It doesn't even explain what operation adjacency represents, eq., ##c^bx##.

Then I am asked to prove that ##(a,b)^-1=(-c^{-b}a,b)##.

I wasn't able to solve it based on the skimpy material in the book.

I searched all over the internet and there is nothing about this formula.

Semidirect products are always defined in a totally different way.

Can anyone point to some examples of using this formula?

It probably won't do any good to explain the theory to me.

I work better the other way around.

When I understand how to do it, then I can understand the theory.