Jim Caprioli at The Finland Station

I wrote an e-mail to David Joyner , if Group Theory was IT he would have been called a Guru. ;-) He is definitely one of the top people in the field.

---

Dear Mr. Joyner,

I have a suggestion for the GAP constructions page:

Question:
"How do I construct a semi-direct product of two groups?"

Answer:
As you can easily verify, D8 is isomorphic to C2:C4. Or in GAP...

N:=CyclicGroup(IsPermGroup,4);
G:=CyclicGroup(IsPermGroup,2);
AutN:=AutomorphismGroup(N);
f:=GroupHomomorphismByImages(G,AutN,GeneratorsOfGroup(G),[Elements(AutN)[2]]);
NG:=SemidirectProduct(G,f,N);

Verify with
StructureDescription(NG);

GAP should return "D8" at this point.

I hope your page will evolve to a tutorial 'plus' or something. The reference is excellent for experienced users, the tutorials are a great way to start with GAP, but what's in between? Your page perhaps?

--
Kind Regards,

---

Why did I write this e-mail in the first place? Simple. I missed the construction rules for a semidirect product on his page.