Finitely generated subgroups of lattices in

Authors:
Yair Glasner, Juan Souto and Peter Storm

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2667-2676

MSC (2010):
Primary 20B15, 20E26, 57N10

DOI:
https://doi.org/10.1090/S0002-9939-10-10310-4

Published electronically:
March 16, 2010

MathSciNet review:
2644883

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Abstract: Let be a lattice in . The pro-normal topology on is defined by taking all cosets of nontrivial normal subgroups as a basis. This topology is finer than the pro-finite topology, but it is not discrete. We prove that every finitely generated subgroup is closed in the pro-normal topology. As a corollary we deduce that if is a maximal subgroup of a lattice in , then either is of finite index or is not finitely generated.

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Additional Information

**Yair Glasner**

Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, 84105 Beer Sheva, Israel

**Juan Souto**

Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-2026

**Peter Storm**

Affiliation:
Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395

DOI:
https://doi.org/10.1090/S0002-9939-10-10310-4

Received by editor(s):
October 26, 2009

Published electronically:
March 16, 2010

Additional Notes:
The first author was partially supported by ISF grant 888/07

The third author was partially supported by a National Science Foundation Postdoctoral Fellowship.

Communicated by:
Alexander N. Dranishnikov

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.