# [GAP Forum] G-invariant linear character

Anvita anvita21 at gmail.com
Fri Apr 25 08:06:51 BST 2008

On Thu, Apr 17, 2008 at 1:42 AM, Dan Lanke <dan_lanke at yahoo.com> wrote:
>
> Dear GAP Forum,
>
> Let H be a normal subgroup of a finite group G.
> Let \rho be a G-invariant linear character of H.
> Is it true that there exists a linear character
> of G whose restriction to H is equal to \rho?
>
> If the answer is no, how can I use GAP to find
> some examples?

Dear Dan,

I think that the answer is "no".
If H is the center (of order 2) of the group G = SL(2,5)
and \rho is the nontrivial character of H, then \rho is G-invariant
but is not the restriction to H of any linear character of G, because
G has only one linear character (the trivial one).

I do not know how to use GAP to find such examples.

Anvita