Premium
Principal congruence subgroups in the infinite rank case
Author(s) -
Tolstykh Vladimir A.
Publication year - 2019
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12250
Subject(s) - congruence (geometry) , mathematics , abelian group , automorphism , group (periodic table) , rank (graph theory) , combinatorics , pure mathematics , general linear group , normal subgroup , symmetric group , geometry , physics , quantum mechanics
Abstract We obtain a number of analogues of the classical results of the 1960s on the general linear groupsGL n ( Z )and special linear groupsSL n ( Z )for the automorphism groupΓ A = 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 subgroupsΓA( m )of the group Aut ( A ) , and obtain an analogue of Brenner's ladder relation for the group Aut ( A ) .