1. Principal congruence subgroups in the infinite rank case.
- Author
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Tolstykh, Vladimir A.
- Subjects
- *
MAXIMAL subgroups , *GENERATORS of groups , *ABELIAN groups , *FREE groups , *GEOMETRIC congruences , *AUTOMORPHISMS , *LINEAR algebraic groups - Abstract
We obtain a number of analogues of the classical results of the 1960s on the general linear groups GL n(Z) and special linear groups SL n(Z) for the automorphism group ΓA=Aut(A) of an infinitely generated free abelian group A. In particular, we obtain a description of normal generators of the group Aut(A), classify the maximal normal subgroups of the group Aut(A), describe normal generators of the principal congruence subgroups ΓA(m) of the group Aut(A), and obtain an analogue of Brenner's ladder relation for the group Aut(A). [ABSTRACT FROM AUTHOR]
- Published
- 2019
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