Groups whose subgroups of infinite rank are closed in the profinite topology

2015 ◽  
Vol 110 (2) ◽  
pp. 565-571
Author(s):  
Maria De Falco ◽  
Francesco de Giovanni ◽  
Carmela Musella
Keyword(s):  
Infinite Rank ◽  
Profinite Topology

scholarly journals TOPOLOGICAL NOETHERIANITY FOR ALGEBRAIC REPRESENTATIONS OF INFINITE RANK CLASSICAL GROUPS

2021 ◽  
Author(s):  
R. H. EGGERMONT ◽  
A. SNOWDEN
Keyword(s):  
Classical Groups ◽  
Infinite Rank ◽  
Polynomial Representations ◽  
Algebraic Representations

AbstractDraisma recently proved that polynomial representations of GL∞ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.

ON THE RANK OF ABELIAN VARIETIES OVER AMPLE FIELDS

2010 ◽  
Vol 06 (03) ◽  
pp. 579-586 ◽  
Author(s):  
ARNO FEHM ◽  
SEBASTIAN PETERSEN
Keyword(s):  
Finite Field ◽  
Abelian Variety ◽  
Galois Extension ◽  
Characteristic Zero ◽  
Rational Point ◽  
Abelian Varieties ◽  
Finitely Generated ◽  
Infinite Rank ◽  
Finite Set

A field K is called ample if every smooth K-curve that has a K-rational point has infinitely many of them. We prove two theorems to support the following conjecture, which is inspired by classical infinite rank results: Every non-zero Abelian variety A over an ample field K which is not algebraic over a finite field has infinite rank. First, the ℤ(p)-module A(K) ⊗ ℤ(p) is not finitely generated, where p is the characteristic of K. In particular, the conjecture holds for fields of characteristic zero. Second, if K is an infinite finitely generated field and S is a finite set of local primes of K, then every Abelian variety over K acquires infinite rank over certain subfields of the maximal totally S-adic Galois extension of K. This strengthens a recent infinite rank result of Geyer and Jarden.

Butler Groups of Infinite Rank II

1990 ◽  
Vol 320 (2) ◽  
pp. 643 ◽  
Author(s):  
Manfred Dugas ◽  
Paul Hill ◽  
K. M. Rangaswamy
Keyword(s):  
Infinite Rank

Near Isomorphism for a Class of Infinite Rank Torsion-Free Abelian Groups

2007 ◽  
Vol 35 (3) ◽  
pp. 1055-1072 ◽  
Author(s):  
Ekaterina Blagoveshchenskaya ◽  
Lutz Strüngmann
Keyword(s):  
Abelian Groups ◽  
Infinite Rank ◽  
Free Abelian Groups ◽  
Torsion Free

Certain Classes of Automorphisms of Infinite Rank Affine Lie Algebras

2005 ◽  
Vol 33 (6) ◽  
pp. 1893-1901
Author(s):  
Jianguo Zha ◽  
Jianhua Hu
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Infinite Rank

Free quotients of infinite rank of GL2 over Dedekind domains

1999 ◽  
Vol 129 (1) ◽  
pp. 77-84
Author(s):  
A. W. Mason
Keyword(s):  
Factor Group ◽  
Krull Dimension ◽  
Two Dimensional ◽  
Integral Domains ◽  
Dimension Zero ◽  
Infinite Rank ◽  
Dedekind Domains ◽  
Free Quotient

This paper is concerned with integral domains R, for which the factor group SL2(R)/U2(R) has a non-trivial, free quotient, where U2(R) is the subgroup of GL2(R) generated by the unipotent matrices. Recently, Krstić and McCool have proved that SL2(P[x])/U2(P[x]) has a free quotient of infinite rank, where P is a domain which is not a field. This extends earlier results of Grunewald, Mennicke and Vaserstein.Any ring of the type P[x] has Krull dimension at least 2. The purpose of this paper is to show that result of Krstić and McCool extends to some domains of Krull dimension 1, in particular to certain Dedekind domains. This result, which represents a two-dimensional anomaly is the best possible in the following sense. It is well known that SL2(R) = U2(R), when R is a domain of Krull dimension zero, i.e. when R is a field. It is already known that for some arithmetic Dedekind domains A, the factor group SL2(A)/U2(A) has a free quotient of finite (and not infinite) rank.

Homology concordance and an infinite rank free subgroup

2021 ◽  
Vol 14 (4) ◽  
pp. 1369-1395
Author(s):  
Hugo Zhou
Keyword(s):  
Free Subgroup ◽  
Infinite Rank

A note on groups of infinite rank whose proper subgroups are abelian-by-finite

2014 ◽  
Vol 137 (2) ◽  
pp. 165-170 ◽  
Author(s):  
Francesco de Giovanni ◽  
Federica Saccomanno
Keyword(s):  
Infinite Rank

Butler groups of infinite rank

1995 ◽  
Vol 98 (1-2) ◽  
pp. 25-44 ◽  
Author(s):  
L Fuchs
Keyword(s):  
Infinite Rank

The Abelian Case of Solitar's Conjecture on Infinite Nielsen Transformations

1985 ◽  
Vol 28 (2) ◽  
pp. 223-230 ◽  
Author(s):  
Olga Macedonska-Nosalska
Keyword(s):  
Abelian Group ◽  
Free Abelian Group ◽  
Infinite Rank ◽  
Abelian Case ◽  
Countably Infinite ◽  
Identical Transformation

AbstractThe paper proves that the group of infinite bounded Nielsen transformations is generated by elementary simultaneous Nielsen transformations modulo the subgroup of those transformations which are equivalent to the identical transformation while acting in a free abelian group. This can be formulated somewhat differently: the group of bounded automorphisms of a free abelian group of countably infinite rank is generated by the elementary simultaneous automorphisms. This proves D. Solitar's conjecture for the abelian case.

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