Duke Mathematical Journal

Golod-Shafarevich groups with property (T) and Kac-Moody groups

Mikhail Ershov

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We construct Golod-Shafarevich groups with property (T) and thus provide counterexamples to a conjecture stated in a recent article of Zelmanov [Z2]. 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 nonamenable groups

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Duke Math. J., Volume 145, Number 2 (2008), 309-339.

First available in Project Euclid: 20 October 2008

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Zentralblatt MATH identifier

Primary: 20E18: Limits, profinite groups
Secondary: 20F05: Generators, relations, and presentations 20E42: Groups with a $BN$-pair; buildings [See also 51E24]


Ershov, Mikhail. Golod-Shafarevich groups with property ( $T$ ) and Kac-Moody groups. Duke Math. J. 145 (2008), no. 2, 309--339. doi:10.1215/00127094-2008-053. https://projecteuclid.org/euclid.dmj/1224508839

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