Geodesic
Cocompact lattices in locally pro-$p$-complete rank-2 Kac-Moody groups
Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1065-1079 Cet article a éte moissonné depuis la source Math-Net.Ru

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We initiate an investigation of lattices in a new class of locally compact groups: so-called locally pro-$p$-complete Kac-Moody groups. We discover that in rank 2 their cocompact lattices are particularly well-behaved: under mild assumptions, a cocompact lattice in this completion contains no elements of order $p$. This statement is still an open question for the Caprace-Rémy-Ronan completion. Using this, modulo results of Capdeboscq and Thomas, we classify edge-transitive cocompact lattices and describe a cocompact lattice of minimal covolume. Bibliography: 22 titles.
Keywords: Kac-Moody group, lattice, building, completion. 
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I. Capdeboscq; K. Hristova; D. A. Rumynin. Cocompact lattices in locally pro-$p$-complete rank-2 Kac-Moody groups. Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1065-1079. http://geodesic.mathdoc.fr/item/SM_2020_211_8_a0/

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