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Normalized matching property of the subgroup lattice of an abelian p-group

2002
*
Discrete Mathematics
*

Let L (k n ) (

doi:10.1016/s0012-365x(02)00514-9
fatcat:ed7spfbqmrfvhhwv6qbpcamnxe
*p*) denote*the**subgroup**lattice**of**the**abelian**p*-*group*In a previous paper (Ann.*of*Combin. 2 (1998) 85), we proved that L (k n ) (*p*) has*the*Sperner*property*. ... In this paper, we prove that for any positive integers n and k, there is a positive integer N (n; k) such that L (k n ) (*p*) has*the**normalized**matching**property*when*p*¿ N (n; k). ...*The*author is also grateful to*the*anonymous referees for their valuable suggestions and corrections. ...##
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Computing Pro-P Galois Groups
[chapter]

2006
*
Lecture Notes in Computer Science
*

We describe methods for explicit computation

doi:10.1007/11792086_1
fatcat:ohnvoxecxraszijnrns4q4bixi
*of*Galois*groups**of*certain tamely ramified*p*-extensions. In*the*finite case this yields a short list*of*candidates for*the*Galois*group*. ... In*the*infinite case it produces a family or few families*of*likely candidates.*The*authors would like to thank Rafe Jones, Jeremy Rouse, Rob Rhoades and Jayce Getz for useful discussions. ...*The**groups*G just found appear always to have a*normal**subgroup*H satisfying G/H ∼ = C 4 and having generator and relation ranks both equal to 4. We call this*the*critical*subgroup**of*G. ...##
###
A new matching property for posets and existence of disjoint chains

2004
*
Journal of combinatorial theory. Series A
*

In this paper, by introducing a new

doi:10.1016/j.jcta.2004.06.002
fatcat:soe7g4jy6zcz7gcdxm5euzrw6i
*matching**property*for posets, called shadow-*matching*, we show that*the*same*property*holds for a much larger class*of*posets including*the*divisor*lattice*,*the*subspace ...*lattice*,*the**lattice**of*partitions*of*a finite set,*the*intersection poset*of*a central hyperplane arrangement,*the*face*lattice**of*a convex polytope,*the**lattice**of*noncrossing partitions, and any geometric ... that*the*poset*of**subgroups**of*a cyclic*group*or*an*elementary*abelian**group*are both shadow-*matching*and hence have*the*Lehman-Ron*property*. ...##
###
Hyperbolic Geometrically Uniform Codes and Ungerboeck Partitioning on the Double Torus

2022
*
Symmetry
*

At least one labeling

doi:10.3390/sym14030449
fatcat:yq6ijo3ttfe4xmi5stu5gl2c2m
*group*was provided for all*of**the*11 regular tessellations on*the*double torus, derived from triangular Fuchsian*groups*, as well as extensions*of*these labeling*groups*to generate ... Furthermore, partitioning chains are constructed into geometrically uniform codes using soluble*groups*as labeling, which in some cases results in*an*Ungerboeck partitioning for*the*surface. ... Conflicts*of*Interest:*The*authors declare no conflict*of*interest. ...##
###
Computation of Galois groups associated to the 2-class towers of some imaginary quadratic fields with 2-class group C2×C2×C2

2009
*
Journal of Number Theory
*

We describe a method for

doi:10.1016/j.jnt.2008.06.007
fatcat:k2qjddpi75d7ljyf534hexcvlm
*the*explicit computation*of*a list*of*possibilities for*the*Galois*group*G*of**an*unramified 2-class tower that combines*the**p*-*group*generation algorithm with algorithms from explicit ... In each case we show that these 2-class towers are finite, and in fact write down for each a short list*of*candidate*groups*for*the*associated Galois*groups*. ...*The*author is supported by*the*Office*of*Naval Research through*an*NDSEG fellowship. ...##
###
The 2-Class Tower of Q(√(-5460))
[article]

2017
*
arXiv
*
pre-print

Using extensive computation and introducing some new techniques, we give strong evidence that

arXiv:1710.10681v1
fatcat:a65dltoz6bhgbfr2uzk3nwmvna
*the*tower is in fact finite, establishing other*properties**of*its Galois*group*en route. ...*The*seminal papers in*the*field*of*root-discriminant bounds are those*of*Odlyzko and Martinet. Both papers include*the*question*of*whether*the*field Q(√(-5460)) has finite or infinite 2-class tower. ... Acknowledgements*The*authors thank Charles Leedham-Green for his comments on*the*paper.*The*first author was supported by Simons Foundation Award MSN-179747. ...##
###
Page 4665 of Mathematical Reviews Vol. , Issue 82k
[page]

1982
*
Mathematical Reviews
*

Any K-realization

*of*G is defined by a*lattice*LC K’ and cl(*p*(G)) is*the*number*of*classes in*the*genus*of*L with respect to G. ... If g€G it is shown that for some j, g”’ lies in a connected*abelian*algebraic*subgroup**of*G. ...##
###
Existence, algorithms, and asymptotics of direct product decompositions, I

2012
*
Groups - Complexity - Cryptology
*

*The*process uses bilinear maps and commutative rings to characterize direct products

*of*

*p*-

*groups*

*of*class 2 and reduces general

*groups*to

*p*-

*groups*using

*group*varieties. ... A polynomial-time algorithm is produced which, given generators for a

*group*

*of*permutations on a finite set, returns a direct product decomposition

*of*

*the*

*group*into directly indecomposable

*subgroups*. ... Hulpke for help with translations and to

*P*. M. Neumann for historical assistence. ...

##
###
LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS

2017
*
Forum of Mathematics, Sigma
*

Given $G\in \mathscr{S}$ , we show that compact open

doi:10.1017/fms.2017.8
fatcat:jyzwy3lmtbbljbduxwyl65tfum
*subgroups**of*$G$ involve finitely many isomorphism types*of*composition factors, and do not have any soluble*normal**subgroup*other than*the*trivial ... By results*of*Part I, this implies that*the*centralizer*lattice*and local decomposition*lattice**of*$G$ are Boolean algebras. ... This research was supported by*an*F.R.S.-FNRS research associate, funded in part by*the*ERC grant #278469, and by*the*ARC Discovery Projects DP0984342 and DP120100996. ...##
###
Automorphic Bloch theorems for finite hyperbolic lattices
[article]

2021
*
arXiv
*
pre-print

representations (irreps)

arXiv:2108.09314v1
fatcat:xssu7h47cfe6zo27kd37pjtdha
*of**the*nonabelian translation*group*, depending on*the**lattice*geometry. ... For a large class*of*finite*lattices*, only one-dimensional irreps appear, and*the*hyperbolic band theory previously developed becomes exact. ...*The*commutator*subgroup*is also*the*smallest*normal**subgroup**of*Γ such that*the*factor*group*is*abelian*; equivalently,*the*quotient Γ/N with N a*normal**subgroup**of*Γ is*abelian*if and only if Γ (1) ⊆ N ...##
###
Pieces of 2d: existence and uniqueness for Barnes–Wall and Ypsilanti lattices

2005
*
Advances in Mathematics
*

We give a new existence proof for

doi:10.1016/j.aim.2004.08.014
fatcat:6webrednrfa3rdgl4p5en2pwyq
*the*rank 2 d even*lattices*usually called*the*Barnes-Wall*lattices*, and establish new results on uniqueness, structure and transitivity*of**the*automorphism*group*on certain ... Our proofs are relatively free*of*calculations, matrix work and counting, due to*the*uniqueness viewpoint. We deduce*the*labeling*of*coordinates on which earlier constructions depend. ... Here are some fairly standard notations used for particular extensions*of**groups*:*p*k means*an*elementary*abelian**p*-*group*; A.B means a*group*extension with*normal**subgroup*A and quotient B;*p*a+b+... means ...##
###
Group-based fields
[chapter]

1996
*
Lecture Notes in Computer Science
*

We are grateful to

doi:10.1007/bfb0023063
fatcat:qyupyzqgynb2hfpelhpfphcbf4
*the*members*of**the*Parallel Architectures team in LRI for many fruitful discussions, and we thank especially Dominique De Vito and Abderrahmane Mahiout. ...*The*hexagonal*lattice*: H2 = (a,b,c; b = a.c) is*an**abelian*shape that can be used for example in image processing (*the*underlying space has*the*Jordan*property*, which is not*the*case for NEWS meshes). ... In*group*based fields,*the*decomposition relies on cosets or on a*normal**subgroup*(which decomposes naturally*the**group*into a product). ...##
###
Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices
[article]

2004
*
arXiv
*
pre-print

We give a new existence proof for

arXiv:math/0403480v1
fatcat:z4xqji3fcvhl3jicekt4i4y2qm
*the*rank 2^d even*lattices*usually called*the*Barnes-Wall*lattices*, and establish new results on uniqueness, structure and transitivity*of**the*automorphism*group*on certain ... Extending these ideas, we construct in dimensions 2^d, for d>>0,*the*Ypsilanti*lattices*, which are families*of*indecomposable even unimodular*lattices*which resemble*the*Barnes-Wall*lattices*. ... Here are some fairly standard notations used for particular extensions*of**groups*:*p*k means*an*elementary*abelian**p*-*group*; A.B means a*group*extension with*normal**subgroup*A and quotient B;*p*a+b+... means ...##
###
Rigidity of group actions on solvable Lie groups

2000
*
Mathematische Annalen
*

Clearly,

doi:10.1007/s002089900091
fatcat:pkqp3nuqynhbdbbwcyrm6uuzt4
*p*is*an*irreducible polynomial, and*the*zeros*of**p*are*the*numbers: 4 √ 3 e iπ/12 , z 2 = −1 + 4 √ 3 e −iπ/12 , z 3 = −1 − 4 √ 3 e iπ/12 , z 4 = −1 − 4 √ 3 e −iπ/12 . ... We establish analogs*of**the*three Bieberbach theorems for a*lattice*Γ in a semidirect product S o K where S is a connected, simply connected solvable Lie*group*and K is a compact*subgroup**of*its automorphism ... But for*an**abelian**group*G*the*proposition is clearly correct. Step 3.*The*proposition is correct if H contains a noncompact, closed,*abelian**normal**subgroup*A. ...##
###
Summaries of articles published in this issue

1978
*
Czechoslovak Mathematical Journal
*

In this paper

doi:10.21136/cmj.1978.101523
fatcat:7lsfg3446nhmvor2bw7ge252ky
*the*relations between*the**properties**of*a*lattice*ordered*group*G and those*of**the*generalized Dedekind completion D^(G}*of*G are investigated. ... ROGER TELLER, Georgetown:*The**lattice**of*solid o-suhgroups*of*a retractable*group*. Czech. Math. ...
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