arithmetic group造句

Arithmetic groups can be used to construct isospectral manifolds.
The hyperbolic triangle groups that are also arithmetic groups form a finite subset.
One of the origins of the mathematical theory of arithmetic groups is algebraic number theory.
Finally arithmetic groups are often used to construct interesting examples of locally symmetric Riemannian manifolds.
The classical example of an arithmetic group is \ mathrm { SL } _ n ( \ mathbb Z ).
It's difficult to find arithmetic group in a sentence. 用arithmetic group造句挺难的

This arithmetic construction can be generalised to obtain the notion of an " S-arithmetic group ".
On the other hand, the class of groups thus obtained is not larger than the class of arithmetic groups as defined above.
Another relevant list is that of K . Takeuchi, who classified the ( hyperbolic ) triangle groups that are arithmetic groups ( 85 examples ).
The existence of congruence subgroups in an arithmetic groups provides it with a wealth of subgroups, in particular it shows that the group is residually finite.
Let \ Gamma _ S be an S-arithmetic group in an algebraic group \ mathbf G \ subset \ mathrm { GL } _ d.
The notion of an arithmetic group is a vast generalisation based upon the fundamental example of \ mathrm { SL } _ d ( \ mathbb Z ).
Using this formula and certain number theoretic and Galois-cohomological estimates, Armand Borel and Gopal Prasad proved several finiteness theorems about arithmetic groups, [ 6 ].
In higher dimensions the problem of finding the lattice of minimal volume is still open, though it has been solved when restricting to the subclass of arithmetic groups.
The family of congruence subgroups in a given arithmetic group " & Gamma; " always has property ( & tau; ) of Lubotzky & ndash; Zimmer.
Let \ Gamma be an arithmetic group : for simplicity it is better to suppose that \ Gamma \ subset \ mathrm { GL } _ n ( \ mathbb Z ).

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