Kazhdan quotients of Golod-Shafarevich groups
نویسندگان
چکیده
منابع مشابه
Kazhdan Quotients of Golod-shafarevich Groups
The main goal of this paper is to prove that every Golod-Shafarevich group has an infinite quotient with Kazhdan’s property (T ). In particular, this gives an affirmative answer to the well-known question about non-amenability of Golod-Shafarevich groups.
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In this paper we survey the main results about Golod-Shafarevich groups and their applications in algebra, number theory and topology.
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We construct Golod-Shafarevich groups with property (T ) and thus provide counterexamples to a conjecture stated in a recent paper of Zelmanov [Ze2]. Explicit examples of such groups are given by lattices in certain topological Kac-Moody groups over finite fields. We provide several applications of this result including examples of residually finite torsion non-amenable groups.
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It is shown that Golod-Shaferevich algebras of a reduced number of defining relations contain noncommutative free subalgebras in two generators, and that these algebras can be homomorphically mapped onto prime, Noetherian algebras with linear growth. It is also shown that Golod-Shafarevich algebras of a reduced number of relations cannot be nil. 2010 Mathematics subject classification: 16P40, 1...
متن کاملNew Kazhdan groups
Introduction A locally compact, second countable group G is called Kazhdan if for any unitary representation of G, the first continuous cohomology group is trivial H 1 ct (G, ρ) = 0. There are several other equivalent definitions, the reader should consult [6], esp. 1.14 and 4.7. For some time now Kazhdan groups have attracted attention. One of the main challenges is to understand them geometri...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2010
ISSN: 0024-6115
DOI: 10.1112/plms/pdq022