- #1
murmillo
- 118
- 0
1. Homework Statement [/b]
I'm reading about semidirect products, and I don't understand this part:
Given two abstract groups H and K and a homomorphism
f : K --> AutH, define a group structure on the Cartesian product H X K
by the rule
(h1, k1) * (h2; k2) = (h1 x f(k1)(h2), k1k2).
I don't understand how how h1 x f(k1)(h2) is an element of H.
3. The Attempt at a Solution [/b]
I think that h1 x f(k1)(h2) is an element of H only when H is normal. But the rule is supposed to work for any two groups H and K.
I'm reading about semidirect products, and I don't understand this part:
Given two abstract groups H and K and a homomorphism
f : K --> AutH, define a group structure on the Cartesian product H X K
by the rule
(h1, k1) * (h2; k2) = (h1 x f(k1)(h2), k1k2).
I don't understand how how h1 x f(k1)(h2) is an element of H.
3. The Attempt at a Solution [/b]
I think that h1 x f(k1)(h2) is an element of H only when H is normal. But the rule is supposed to work for any two groups H and K.