Hi There,(adsbygoogle = window.adsbygoogle || []).push({});

Ok, I'm new to this so i'm sorry if this is abit warbled!...

We have a normal subgroup N of a finite group H such that [H:N]=2

We have a chatacter Chi belonging to the irreducible characters of H, Irr(H) , which is zero on H\N.

I have already shown that Chi restricted to N = Theta 1 + Theta 2, Where

Theta 1 is not equal to Theta 2, and both Theta 1, and Theta 2 belong to Irr(N).

I am now trying to show that given a conjugacy class K of H which is also a conjugacy class of N, we get Theta 1 (n) = Theta 2 (n) for n a member of K.

Intuitively, I can see this is true, I have seen examples in the alternating group A6, the normal subgroup of index 2 in S6 fro example.

I would be really greatful for a push in the right direction...I have books: 'James and Liebeck' and 'Isaacs'... if you could even direct me to some relevant info?

Wow, think my notation is abit crap, sorry.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Characters of Normal Subgroup of Index 2

Loading...

Similar Threads for Characters Normal Subgroup |
---|

I Eigenproblem for non-normal matrix |

I Proving only 1 normalized unitary vector for normal matrix |

A Why a Lie Group is closed in GL(n,C)? |

I Normal modes using representation theory |

**Physics Forums | Science Articles, Homework Help, Discussion**