Re: Centralizers, Normalizers and the Center
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Thu, 7 Jul 2005 16:56:21 +0000 (UTC)
In article <24084316.1120699807491.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Lawrence House <lawrence.house@xxxxxxxxxxx> wrote:
>I'm confused by the notation. Is C_H(G). Is it (1) the set of all
elements in H which commute with all of G? or (2) Z(H) the
centralizer of H?
Ehr, C_H(G) is usually the set of all elements in H that commute with
each (all) elements of G. Z(H) is normally the CENTER of H, that is,
the elements of H that commute with every element in H.
Since you did not quote the original, however, it seems hard to say
what the original meaning was meant to be.
> If (1) it is the intersection of Z(G) with H and
>therefore a subgroup of G. If (2) it is a subgroup of H and therefore
>again a subgroup of G.
>Also what is meant by N_H(G)? Might this be the set of all elements
of G that commute with all elements of H?
N_H(G) is usually the normalizer in H of G: all elements h in H such
that hGh^{-1}=G.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx
.
- References:
- Centralizers, Normalizers and the Center
- From: themadhatter012
- Re: Centralizers, Normalizers and the Center
- From: Lawrence House
- Centralizers, Normalizers and the Center
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