Kazhdan constants of group extensions. (English) Zbl 1253.20031
Summary: We give bounds on Kazhdan constants of Abelian extensions of (finite) groups. As a corollary, we improve known results of Kazhdan constants for some meta-Abelian groups and for the relatively free group in the variety of \(p\)-groups of lower \(p\)-series of class 2. Furthermore, we calculate Kazhdan constants of the tame automorphism groups of the free nilpotent groups.
MSC:
| 20F05 | Generators, relations, and presentations of groups |
| 20E22 | Extensions, wreath products, and other compositions of groups |
| 20F65 | Geometric group theory |
| 22E46 | Semisimple Lie groups and their representations |
Keywords:
Kazhdan property (T); Kazhdan constants; unitary representations; group extensions; tame automorphism groups; free nilpotent groupsReferences:
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