Re: coset~.

From: William Elliot (marsh_at_privacy.net)
Date: 07/29/04 

Date: Thu, 29 Jul 2004 04:50:07 -0700

On Thu, 29 Jul 2004, mina_world wrote:
> "mina_world" <mina_world@hanmail.net> wrote in message
> >
> > Note that every subgroup H containing just half
> > the elements of a finite group G must be a normal subgroup
> >
> > since for each element a in G but not in H,
> > both the left coset "aH" and the right coset "Ha" must consist of
> > all elements in G that are not in H.
> >
> > Thus the left and right cosets of H coincide and
> > H is a normal subgroup of G.
> >
> > "both the left coset "aH" and the right coset "Ha" must consist of
> > all elements in G that are not in H."
>
> i can't understand this part.
>
It's because cosets are equinumerous.

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