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Results tagged with abelian-groups
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user 4149
For questions about groups whose elements commute.
9
votes
Accepted
$N_{G}(E)/C_{G}(E)$ is the Weyl group of $G$?
$\newcommand{\ZZ}{{\mathcal Z}_G}
\newcommand{\NN}{{\mathcal N}_G}
\newcommand{\zz}{{\mathfrak z}_G}
\newcommand{\Lie}{{\rm Lie\,}}
\renewcommand{\tt}{{\mathfrak t}}
\renewcommand{\gg}{{\mathfrak g}}
…
- 14.2k
4
votes
0
answers
109
views
Duality for finite quotient groups of finitely generated free abelian groups
$\newcommand{\Z}{{\Bbb Z}}
\newcommand{\Q}{{\Bbb Q}}
\newcommand{\Hom}{{\rm Hom}}
$ The following lemma is certainly known.
Lemma (well-known).
Let $B$ be a lattice (that is, a finitely generated fre …
- 14.2k
4
votes
0
answers
63
views
Possible questions about the Tate-Shafarevich subgroup of a Galois hypercohomology group?
$\newcommand{\wt}{\widetilde}$
Let $n=1,2$. There are infinite torsion abelian groups $H^1$, $H^2$ killed by some natural number $m$.
There are finite subgroups
$$ {\rm Sha}^1 \subset H^1,\quad …
- 14.2k
1
vote
0
answers
92
views
A duality of finite groups coming from a surjective homomorphism with finite kernel of algeb...
$\newcommand{\Hom}{{\rm Hom}}
\newcommand{\Gm}{{{\mathbb G}_{m,{\Bbb C}}}}
\newcommand{\X}{{\sf X}}
$ I am looking for a reference for the following lemma (for which I know a proof):
Lemma.
Let $\var …
- 14.2k