scholarly journals On primordial groups for the Green ring

2012 ◽  
Vol 56 (1) ◽  
pp. 337-347
Author(s):  
Alberto G. Raggi-Cárdenas ◽  
Nadia Romero
Keyword(s):  
Finite Group ◽  
Finitely Generated ◽  
Green Ring ◽  
Mackey Functor ◽  
The Family

AbstractConsider the Mackey functor that assigns to each finite group G the Green ring of finitely generated kG-modules, where k is a field of characteristic p > 0. Thévenaz foresaw in 1988 that the class of primordial groups for this functor is the family of k-Dress groups. In this paper we prove that this is true for the subfunctor defined by the Green ring of finitely generated kG-modules of trivial source.

Primitivity in representations of polycyclic groups

1980 ◽  
Vol 88 (1) ◽  
pp. 15-31 ◽  
Author(s):  
D. L. Harper
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Nilpotent Group ◽  
Infinite Dimension ◽  
Finitely Generated ◽  
Polycyclic Groups

In an earlier paper (5) we showed that a finitely generated nilpotent group which is not abelian-by-finite has a primitive irreducible representation of infinite dimension over any non-absolute field. Here we are concerned primarily with the converse question: Suppose that G is a polycyclic-by-finite group with such a representation, then what can be said about G?

scholarly journals A note on the fixed subring of an FPF ring

1989 ◽  
Vol 40 (1) ◽  
pp. 109-111 ◽  
Author(s):  
John Clark
Keyword(s):  
Finite Group ◽  
Associative Ring ◽  
Finitely Generated ◽  
Group Of Automorphisms ◽  
Direct Sum ◽  
Epimorphic Image ◽  
A Finite Group

An associative ring R with identity is called a left (right) FPF ring if given any finitely generated faithful left (right) R-module A and any left (right) R-module M then M is the epimorphic image of a direct sum of copies of A. Faith and Page have asked if the subring of elements fixed by a finite group of automorphisms of an FPF ring need also be FPF. Here we present examples showing the answer to be negative in general.

scholarly journals Inertial subalgebras of algebras possessing finite automorphism groups

1979 ◽  
Vol 28 (3) ◽  
pp. 335-345 ◽  
Author(s):  
Nicholas S. Ford
Keyword(s):  
Finite Group ◽  
Commutative Ring ◽  
Jacobson Radical ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finitely Generated ◽  
Fixed Ring ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractLet R be a commutative ring with identity, and let A be a finitely generated R-algebra with Jacobson radical N and center C. An R-inertial subalgebra of A is a R-separable subalgebra B with the property that B+N=A. Suppose A is separable over C and possesses a finite group G of R-automorphisms whose restriction to C is faithful with fixed ring R. If R is an inertial subalgebra of C, necessary and sufficient conditions for the existence of an R-inertial subalgebra of A are found when the order of G is a unit in R. Under these conditions, an R-inertial subalgebra B of A is characterized as being the fixed subring of a group of R-automorphisms of A. Moreover, A ⋍ B ⊗R C. Analogous results are obtained when C has an R-inertial subalgebra S ⊃ R.

The mod ℭ Suspension Theorem

1969 ◽  
Vol 21 ◽  
pp. 684-701 ◽  
Author(s):  
Benson Samuel Brown
Keyword(s):  
Finite Group ◽  
Exact Sequence ◽  
Abelian Groups ◽  
Finitely Generated ◽  
Finite Abelian Groups ◽  
Cw Complexes ◽  
Image Position ◽  
A Finite Group

Our aim in this paper is to prove the general mod ℭ suspension theorem: Suppose that X and Y are CW-complexes,ℭ is a class offinite abelian groups, and that(i) πi(Y) ∈ℭfor all i < n,(ii) H*(X; Z) is finitely generated,(iii) Hi(X;Z) ∈ℭfor all i > k.Then the suspension homomorphismis a(mod ℭ) monomorphism for 2 ≦ r ≦ 2n – k – 2 (when r= 1, ker E is a finite group of order d, where Zd∈ ℭ and is a (mod ℭ) epimorphism for 2 ≦ r ≦ 2n – k – 2The proof is basically the same as the proof of the regular suspension theorem. It depends essentially on (mod ℭ) versions of the Serre exact sequence and of the Whitehead theorem.

Simple groups and irreducible lattices in wreath products

2020 ◽  
pp. 1-12 ◽  
Author(s):  
ADRIEN LE BOUDEC
Keyword(s):  
Finite Group ◽  
Wreath Product ◽  
Free Group ◽  
Wreath Products ◽  
Simple Groups ◽  
Finitely Generated ◽  
Locally Compact ◽  
Regular Tree ◽  
Finitely Generated Groups ◽  
A Finite Group

We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of finitely generated simple groups quasi-isometric to a wreath product $C\wr F$ , where $C$ is a finite group and $F$ a non-abelian free group.

scholarly journals Locally graded groups with all subgroups normal-by-finite

1996 ◽  
Vol 60 (2) ◽  
pp. 222-227 ◽  
Author(s):  
Howard Smith ◽  
James Wiegold
Keyword(s):  
Finite Group ◽  
Finite Index ◽  
Finitely Generated ◽  
Locally Finite ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Open Question ◽  
Locally Graded Groups

AbstractIn a paper published in this journal [1], J. T. Buckely, J. C. Lennox, B. H. Neumann and the authors considered the class of CF-groups, that G such that |H: CoreG (H)| is finite for all subgroups H. It is shown that locally finite CF-groups are abelian-by-finite and BCF, that is, there is an integer n such that |H: CoreG(H)| ≤ n for all subgroups H. The present paper studies these properties in the class of locally graded groups, the main result being that locally graded BCF-groups are abelian-by-finite. Whether locally graded CF-groups are BFC remains an open question. In this direction, the following problems is posed. Does there exist a finitely generated infinite periodic residually finite group in which all subgroups are finite or of finite index? Such groups are locally graded and CF but not BCF.

scholarly journals Genomic Analyses of Cherry Rusty Mottle Group and Cherry Twisted Leaf-Associated Viruses Reveal a Possible New Genus Within the FamilyBetaflexiviridae

2015 ◽  
Vol 105 (3) ◽  
pp. 399-408 ◽  
Author(s):  
D. E. V. Villamor ◽  
J. Susaimuthu ◽  
K. C. Eastwell
Keyword(s):  
New Genus ◽  
High Throughput Sequencing ◽  
Prunus Avium ◽  
Triple Gene Block ◽  
Mottle Virus ◽  
Virus Species ◽  
Gene Block ◽  
Green Ring ◽  
The Family ◽  
Prunus Spp

It is demonstrated that closely related viruses within the family Betaflexiviridae are associated with a number of diseases that affect sweet cherry (Prunus avium) and other Prunus spp. Cherry rusty mottle-associated virus (CRMaV) is correlated with the appearance of cherry rusty mottle disease (CRMD), and Cherry twisted leaf-associated virus (CTLaV) is linked to cherry twisted leaf disease (CTLD) and apricot ringpox disease (ARPD). Comprehensive analysis of previously reported full genomic sequences plus those determined in this study representing isolates of CTLaV, CRMaV, Cherry green ring mottle virus, and Cherry necrotic rusty mottle virus revealed segregation of sequences into four clades corresponding to distinct virus species. High-throughput sequencing of RNA from representative source trees for CRMD, CTLD, and ARPD did not reveal additional unique virus sequences that might be associated with these diseases, thereby further substantiating the association of CRMaV and CTLaV with CRMD and CTLD or ARPD, respectively. Based on comparison of the nucleotide and amino acid sequence identity values, phylogenetic relationships with other triple-gene block-coding viruses within the family Betaflexiviridae, genome organization, and natural host range, a new genus (Robigovirus) is suggested.

On locally nilpotent groups

1956 ◽  
Vol 52 (1) ◽  
pp. 5-11 ◽  
Author(s):  
D. H. McLain ◽  
P. Hall
Keyword(s):  
Finite Group ◽  
Nilpotent Group ◽  
Direct Product ◽  
Finite Subset ◽  
Nilpotent Groups ◽  
Finitely Generated ◽  
Locally Finite ◽  
Locally Nilpotent Groups ◽  
Locally Nilpotent ◽  
A Finite Group

1. If P is any property of groups, then we say that a group G is ‘locally P’ if every finitely generated subgroup of G satisfies P. In this paper we shall be chiefly concerned with the case when P is the property of being nilpotent, and will examine some properties of nilpotent groups which also hold for locally nilpotent groups. Examples of locally nilpotent groups are the locally finite p-groups (groups such that every finite subset is contained in a finite group of order a power of the prime p); indeed, every periodic locally nilpotent group is the direct product of locally finite p-groups.

scholarly journals APPROXIMATING THE FIRST L2-BETTI NUMBER OF RESIDUALLY FINITE GROUPS

2011 ◽  
Vol 03 (02) ◽  
pp. 153-160 ◽  
Author(s):  
W. LÜCK ◽  
D. OSIN
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Betti Number ◽  
Betti Numbers ◽  
Torsion Group ◽  
Normal Subgroups ◽  
Finitely Generated ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Residually Finite Groups

We show that the first L2-betti number of a finitely generated residually finite group can be estimated from below by using ordinary first betti numbers of finite index normal subgroups. As an application, we construct a finitely generated infinite residually finite torsion group with positive first L2-betti number.

scholarly journals Viruses Associated with Rusty Mottle and Twisted Leaf Diseases of Sweet Cherry Are Distinct Species

2013 ◽  
Vol 103 (12) ◽  
pp. 1287-1295 ◽  
Author(s):  
D. E. V. Villamor ◽  
K. C. Eastwell
Keyword(s):  
Distinct Species ◽  
Mottle Virus ◽  
Distribution Data ◽  
Virus Species ◽  
Rna Sequences ◽  
Sequence Comparisons ◽  
Protein Coding ◽  
Green Ring ◽  
Virus Rna ◽  
The Family

Virus RNA sequences related to those of the family Betaflexiviridae were amplified from trees affected with the following diseases: cherry twisted leaf, apricot ring pox, cherry necrotic rusty mottle, cherry rusty mottle, and cherry green ring mottle. Phylogenetic analysis of virus sequences obtained from these diseased trees from western North America, along with published sequences of Cherry green ring mottle virus (CGRMV) and Cherry necrotic rusty mottle virus (CNRMV), revealed four major clades. Segregation into these four populations correlated with distinct symptom expression on woody indicators, suggesting that each clade represents a distinct virus species within the family Betaflexiviridae. The viruses occupying each clade were designated clade I: Cherry twisted leaf associated virus, clade II: CNRMV, clade III: Cherry rusty mottle associated virus, and clade IV: CGRMV. Potential recombination events were predicted to occur within and between these viruses, the latter being strongly supported by incongruent phylogenies. Examination of frequency distribution data derived from pairwise sequence comparisons of coat protein coding sequences resulted in a proposal for alternative guidelines for species demarcation for this family of viruses.

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