Is <(12)> a Maximal Subgroup of S_{3}?

Thread starter moont14263
Start date Dec 7, 2011
Tags

Group Subgroup

Dec 7, 2011

moont14263

If G is a finite group and M is a maximal subgroup, H is a subgroup of G not contained in M. Then G=HM.

Is this true?

Physics news on Phys.org

Dec 7, 2011

micromass

Staff Emeritus

Science Advisor

Homework Helper

Insights Author

No. Can you find a counterexample?

Dec 7, 2011

moont14263

I tried, but I failed. Thanks.

Dec 7, 2011

micromass

Staff Emeritus

Science Advisor

Homework Helper

Insights Author

What could go wrong??

Dec 7, 2011

moont14263

S_{3}, <(12)> maximal, <(23)>, S_{3} not equal <(12)><(23)>
Thank you very much.

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

View full post »

Thread 'Solve this problem that involves induction'

Hello, This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread. Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).

View full post »