Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I need an example of a finite group $G$ such that

1) the number of Sylow $p$-subgroup of $G$ is $1$ for all $p\neq 2$

2) the number of Sylow $2$-subgroup of $G$ is $3$.

share|improve this question
1  
What are their motivations with these questions? –  Elias Mar 22 '13 at 16:05
1  
What do you need the group for? What are your thoughts on how one might construct one? –  Tobias Kildetoft Mar 22 '13 at 16:05
2  
Try the smallest possible example!! –  user641 Mar 22 '13 at 16:07
    
To follow up on @SteveD's comment, (2) tells you that the group is non-abelian. Think of the non-abelian (small) group(s) you know. –  Andreas Caranti Mar 22 '13 at 16:12

1 Answer 1

Hints (in the correct order): any finite abelian group, non-abelian group of order $\,6\,$ ...

share|improve this answer
    
I take OP wants a single group that satisfies both conditions. –  Andreas Caranti Mar 22 '13 at 16:28
    
Ok, then only the second hinted one (the smallest non-abelian group) –  DonAntonio Mar 22 '13 at 16:31

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.