Infinite families of isomorphic nonconjugate finitely generated subgroups

Author:
F. E. A. Johnson

Journal:
Trans. Amer. Math. Soc. **342** (1994), 397-406

MSC:
Primary 20E07

MathSciNet review:
1154542

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Abstract: Let be a nondegenerate symmetric bilinear form on a finitely generated free abelian group *L* which splits as an orthogonal direct sum in which has signature (2, 1), has signature (*n*, 1) with , and is either zero or indefinite with . We show that the integral automorphism group contains an infinite family of mutually isomorphic finitely generated subgroups , no two of which are conjugate. In the simplest case, when , the groups are all normal subdirect products in a product of free groups or surface groups. The result can be seen as a failure of the rigidity property for subgroups of infinite covolume within the corresponding Lie group .

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1994-1154542-6

Article copyright:
© Copyright 1994
American Mathematical Society