例句與造句

1. It is easily seen from the basic theory of group actions on trees that uniform tree lattices are virtually free groups.
2. Thus the more interesting tree lattices are the non-uniform ones, equivalently those for which the quotient graph \ Gamma \ backslash T is infinite.
3. The theory of tree lattices turns out to be useful in the study of discrete subgroups of algebraic groups over non-archimedean local fields and in the study of Kac Moody groups.
4. The theory of " tree lattices " was developed by Bass, Kulkarni and lattices in Lie groups ( that is discrete subgroups of Lie groups of finite co-volume ).
5. A "'lattice "'in a locally compact topological group is a discrete subgroup with the property that the Lubotzky initiated the study of " tree lattices ", which remains an active research area.
6. It's difficult to find tree lattice in a sentence. 用tree lattice造句挺難的
7. Lattices are also well-studied in some other classes of groups, in particular groups associated to Kac-Moody algebras and automorphisms groups of regular trees ( the latter are known as " tree lattices " ).
8. If \ Gamma is the fundamental group of an infinite graph of groups, all of whose vertex groups are finite, and under additional necessary assumptions on the index of the edge groups and the size of the vertex groups, then the action of \ Gamma on the Bass-Serre tree associated to the graph of groups realises it as a tree lattice.
9. The general existence theorem is more subtle : it is necessary and sufficient that H be unimodular, and that the quotient H \ backslash T be of " finite volume " in a suitable sense ( which can be expressed combinatorially in terms of the action of H ), more general than the stroger condition that the quotient be finite ( as proven by the very existence of nonuniform tree lattices ).