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The top homology of the lattice of subgroups of a soluble group

1985
*
Discrete Mathematics
*

Introduction Let G be

doi:10.1016/s0012-365x(85)80005-4
fatcat:vwkkzr56zzdhhlkyklsbqzansm
*a*finite*group*, L(G)*the**lattice**of*all*subgroups**of*G and L(G) = L(G)- (1, G}*the*poset*of*non-trivial proper*subgroups**of*G. ...*The*description*of**the*G-module structure*of**the**top**homology*will be complete if we find*the*orbits in*the*G-set r. ...##
###
Page 4507 of Mathematical Reviews Vol. , Issue 86j
[page]

1986
*
Mathematical Reviews
*

*The*latter gives information on

*the*algebraic K-theory

*of*noncommutative local rings.” Thévenaz, Jacques (CH-LAUS) 86j:20045

*The*

*top*

*homology*

*of*

*the*

*lattice*

*of*

*subgroups*

*of*

*a*

*soluble*

*group*. ... In

*the*present work,

*a*description

*of*

*the*action

*of*G on

*the*

*top*-dimensional

*homology*is given. ...

##
###
On the homotopy type of the Quillen complex of finite soluble groups

2005
*
Journal of Algebra
*

We prove that

doi:10.1016/j.jalgebra.2004.08.035
fatcat:w6kfn6mqdjgslkcfgpj62r7aay
*the*homotopy type*of**the*Quillen complex*of**a*finite*soluble**group*at*the*prime p = 2 is that*of**a*wedge*of*spheres*of*possible different dimensions. 2004 Elsevier Inc. ... I also thank Sandro Buoncristiano for suggesting me*the*proof*of*Proposition 11. ... nth*homology**groups**of*X ∨ Y and S. ...##
###
Page 4842 of Mathematical Reviews Vol. , Issue 87i
[page]

1987
*
Mathematical Reviews
*

87i:20067

*The*proofs use*homological*techniques.*The*paper ends with*a*number*of*examples showing that*the*results cannot be improved for finite-by-nilpotent*groups*. J.*A*. ...*The*3-orbit*groups*which are not*of*prime-power order are classified. It is shown that*A*; is*the*only insoluble 4-orbit*group*, and*a*structure theorem is proved for*soluble*4-orbit*groups*.” ...##
###
Bredon-Poincare Duality Groups
[article]

2014
*
arXiv
*
pre-print

all finite

arXiv:1311.7629v2
fatcat:jias7ttdgjhcpe73tvbinqafbm
*subgroups*H*of*G. ... duality*groups*arising from actions on manifolds M where*the*dimensions*of**the*submanifolds M^H are specified. ... In [Rag84][Rag95], examples*of*cocompact*lattices*in finite covers*of**the*Lie*group*Spin(2, n) are given which are not virtually torsion-free. 4.6. Virtually*Soluble**Groups*. ...##
###
The Homological Invariants for Metabelian Groups of Finite Prüfer Rank: A Proof of the Σm -Conjecture

1996
*
Proceedings of the London Mathematical Society
*

All three applications

doi:10.1112/plms/s3-72.2.385
fatcat:haig54bfofau5c4ftdsd6tvd4q
*of*our new criterion are needed for*the*proof*of*Theorem*A*in § 6. Some*of*our results also hold for*soluble*-by-finite*groups**of*type FP^. Recall that, by*a*recent result*of*P. ... Our first application*of*this Z m -criterion yields*a*new characterization*of**the*higher*homological*invariants in terms*of**a*filtration*of**the*(infinite) simplex spanned by*the**group*G by subcomplexes ... Let G be*a*finitely generated*soluble*-by-finite*group**of*finite Priifer rank, and let N be*a*normal*subgroup**of*G with abelian quotient. ...##
###
The Aquaporins, Blueprints for Cellular Plumbing Systems

1998
*
Journal of Biological Chemistry
*

While purifying

doi:10.1074/jbc.273.24.14659
pmid:9614059
fatcat:53bsgop3xbdzvoxllpqtkze5fe
*the*32-kDa subunit*of**the*red cell Rh blood*group*antigen,*a*new 28-kDa polypeptide was discovered (2). ... Detailed biochemical studies*of*this newly identified tetrameric membrane protein were made easy by its low*solubility*in N-lauroylsarcosine, which permitted simple purification (3). ...*The*existence*of*independent water and glycerol transporting domains was suggested by one*group**of*scientists;*the*existence*of**a*single pore was suggested by*a*second*group*;*a*third*group*incorrectly ...##
###
Finiteness properties of soluble arithmetic groups over global function fields

2004
*
Geometry and Topology
*

Let G be

doi:10.2140/gt.2004.8.611
fatcat:lhgijvlzbfhcbecuzrhv5vtbqq
*a*Chevalley*group*scheme and B<=G*a*Borel*subgroup*scheme, both defined over Z. ... Then,*the*S-arithmetic*group*B(O_S) is*of*type F_|S|-1 but not*of*type FP_|S|. Moreover one can derive lower and upper bounds for*the*geometric invariants Σ^m(B(O_S)). ...*Soluble**groups*, eg,*groups**of*upper triangular matrices form*the*other extreme. ...##
###
Prediction of cloud condensation nuclei activity for organic compounds using functional group contribution methods

2015
*
Geoscientific Model Development Discussions
*

Simulation

doi:10.5194/gmdd-8-7445-2015
fatcat:bldcvpddqnazvhtgqarwte5boq
*of**homologous*series is used to identify*the*relative effectiveness*of*different functional*groups*in increasing*the*CCN activity*of*weakly functionalized organic compounds. ... This work describes*a*model to predict*the*CCN activity*of*organic compounds from functional*group*composition. ... This work was funded by*the*Department*of*Energy, Office*of*Biological and Environmental Sciences under grant DE-SC0010470. Edited by:*A*. Archibald ...##
###
Prediction of cloud condensation nuclei activity for organic compounds using functional group contribution methods

2016
*
Geoscientific Model Development
*

Simulation

doi:10.5194/gmd-9-111-2016
fatcat:ul4oayl42fhmxjbjzyzcxiywea
*of**homologous*series is used to identify*the*relative effectiveness*of*different functional*groups*in increasing*the*CCN activity*of*weakly functionalized organic compounds. ... This work describes*a*model to predict*the*CCN activity*of*organic compounds from functional*group*composition. ... This work was funded by*the*Department*of*Energy, Office*of*Biological and Environmental Sciences under grant DE-SC0010470. Edited by:*A*. Archibald ...##
###
Metabelianisations of finitely presented groups
[article]

2018
*
arXiv
*
pre-print

*The*considered classes include those

*of*

*soluble*

*groups*,

*of*one-relator or knot

*groups*, and

*of*Artin

*groups*. ... In this article, I study some classes

*of*finitely presented

*groups*with

*the*aim

*of*finding out whether

*the*maximal metabelian quotients

*of*

*the*members

*of*these classes admit finite presentations. ... Being

*soluble*is

*a*property which rules out that

*the*

*group*in question does contain

*a*non-abelian-free

*subgroup*; being

*a*member

*of*

*a*variety

*of*

*groups*distinct from

*the*variety

*of*all

*groups*has

*the*same ...

##
###
Brouwer degree, domination of manifolds, and groups presentable by products
[article]

2016
*
arXiv
*
pre-print

Löh:

arXiv:1609.06637v1
fatcat:wvqigvlwjnb7naj43zbt2k7wxa
*a**group*is presentable by*a*product if it contains two infinite commuting*subgroups*which generate*a**subgroup**of*finite index. ...*The*last section shows*a*small sample*of**groups*which are not presentable by products; examples include appropriate Coxeter*groups*. ... (*a*consequence*of**the*Cartan-Hadamard theorem); (1.iv) all manifolds*of**the*form Γ\G/K, with G*a*connected Lie*group*, K*a*maximal compact*subgroup**of*G, and Γ*a*torsion-free cocompact*lattice*in G (*a*...##
###
Topology of plane algebraic curves: the algebraic approach
[article]

2009
*
arXiv
*
pre-print

We discuss

arXiv:0907.0289v1
fatcat:ouoxcfnwfzfi3jqiki3dooggdm
*the*principle tools and results and state*a*few open problems concerning*the*classification and topology*of*plane sextics and trigonal curves in ruled surfaces. ... If X =X C for*a*simple sextic C ⊂ P 2 and E are*the*exceptional divisors contracted in P 2 , then*the**group*in question is an index 2*subgroup**of*π 1 (P 2 C)/δ 2 , where δ is*the*class*of**a*meridian. ...*of*oriented abstract*homological*types (H, o) with*a*prescribed*group*G*of*(anti-)automorphisms. ...##
###
Positive-entropy integrable systems and the Toda lattice, II

2010
*
Mathematical proceedings of the Cambridge Philosophical Society (Print)
*

*A*central role is played by

*the*Lax representation

*of*

*a*Bogoyavlenskij-Toda

*lattice*. ...

*The*classification

*of*these systems, up to iso-energetic topological conjugacy, is related to

*the*classification

*of*abelian

*groups*

*of*Anosov toral automorphisms by their topological entropy function. ... From this, there is

*a*natural Lie

*group*structure on R b ⋆

*A*R =: S and Z b ⋆

*A*=: S Z is

*a*

*lattice*

*subgroup*

*of*S, c.f. 2.2. ...

##
###
Structural, Evolutionary, and Assembly Principles of Protein Oligomerization
[chapter]

2013
*
Progress in Molecular Biology and Translational Science
*

In Section 2, we describe

doi:10.1016/b978-0-12-386931-9.00002-7
pmid:23663964
fatcat:fbnllfrbsfdjleod2wujqsddaq
*the*morphological properties*of*homomers, as well as*the*database 3DComplex, which provides*a*taxonomy for both homomeric and heteromeric protein complexes. ...*The*prevalence*of*homomers motivates us to review many*of*their properties. ... At*the**top*most level,*the*similarity*of*simple features is sufficient to*group*complexes, and these*groups*are split into*subgroups*toward*the*bottom*of**the*hierarchy, where similarity*of*more detailed ...
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