Welcome to MathOverflow

Question

1

Hi,

Is there any way to classify finite non-abelian groups of order p^3q with p and q primes?

Thanks.

edited May 3 2011 at 22:48

asked May 3 2011 at 22:27

jorgeecardona
11●2

4

Yes, either a Sylow p-group is normal or a Sylow q-group is normal, unless your group has order 24. – Steve D May 3 2011 at 22:45

3

And even in the order 24 case, $S_4$ is the only exception. – Steve D May 3 2011 at 22:46

2

This is indeed a well known fact. In case you want a reference, I can strongly recommend Martin Isaac's book "Finite Group Theory". The theorem that Steve mentioned is in Theorems 1.32 and 1.33 of that book. – Tom De Medts May 4 2011 at 7:18

mt · Answer 1 · 2011-05-08 10:36:53Z UTC

If you would like a historical reference, Burnside in his book cites Western, "Groups of order $p^3q$", Proc. LMS Vol xxx. 1899 pp. 209--263, But the length of that paper suggests another source would be better if all you want is the result...

Finite groups of the form p^3q

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.