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

Jun Wang
2002 Discrete Mathematics  
Let L (k n ) (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.  ... 
doi:10.1016/s0012-365x(02)00514-9 fatcat:ed7spfbqmrfvhhwv6qbpcamnxe

Computing Pro-P Galois Groups [chapter]

Nigel Boston, Harris Nover
2006 Lecture Notes in Computer Science  
We describe methods for explicit computation 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.  ... 
doi:10.1007/11792086_1 fatcat:ohnvoxecxraszijnrns4q4bixi

A new matching property for posets and existence of disjoint chains

Mark J. Logan, Shahriar Shahriari
2004 Journal of combinatorial theory. Series A  
In this paper, by introducing a new 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.  ... 
doi:10.1016/j.jcta.2004.06.002 fatcat:soe7g4jy6zcz7gcdxm5euzrw6i

Hyperbolic Geometrically Uniform Codes and Ungerboeck Partitioning on the Double Torus

Eduardo Michel Vieira Gomes, Edson Donizete de Carvalho, Carlos Alexandre Ribeiro Martins, Waldir Silva Soares, Eduardo Brandani da Silva
2022 Symmetry  
At least one labeling 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.  ... 
doi:10.3390/sym14030449 fatcat:yq6ijo3ttfe4xmi5stu5gl2c2m

Computation of Galois groups associated to the 2-class towers of some imaginary quadratic fields with 2-class group C2×C2×C2

Harris Nover
2009 Journal of Number Theory  
We describe a method for 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.  ... 
doi:10.1016/j.jnt.2008.06.007 fatcat:k2qjddpi75d7ljyf534hexcvlm

The 2-Class Tower of Q(√(-5460)) [article]

Nigel Boston, Jiuya Wang
2017 arXiv   pre-print
Using extensive computation and introducing some new techniques, we give strong evidence that 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.  ... 
arXiv:1710.10681v1 fatcat:a65dltoz6bhgbfr2uzk3nwmvna

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

James B. Wilson
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.  ... 
doi:10.1515/gcc-2012-0007 fatcat:bkygvmmqgjh3lco26snffbccau


2017 Forum of Mathematics, Sigma  
Given $G\in \mathscr{S}$ , we show that compact open 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.  ... 
doi:10.1017/fms.2017.8 fatcat:jyzwy3lmtbbljbduxwyl65tfum

Automorphic Bloch theorems for finite hyperbolic lattices [article]

Joseph Maciejko, Steven Rayan
2021 arXiv   pre-print
representations (irreps) 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  ... 
arXiv:2108.09314v1 fatcat:xssu7h47cfe6zo27kd37pjtdha

Pieces of 2d: existence and uniqueness for Barnes–Wall and Ypsilanti lattices

Robert L. Griess
2005 Advances in Mathematics  
We give a new existence proof for 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  ... 
doi:10.1016/j.aim.2004.08.014 fatcat:6webrednrfa3rdgl4p5en2pwyq

Group-based fields [chapter]

Jean-Louis Giavitto, Olivier Michel, Jean-Paul Sansonnet
1996 Lecture Notes in Computer Science  
We are grateful to 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).  ... 
doi:10.1007/bfb0023063 fatcat:qyupyzqgynb2hfpelhpfphcbf4

Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices [article]

Robert L. Griess Jr
2004 arXiv   pre-print
We give a new existence proof for 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  ... 
arXiv:math/0403480v1 fatcat:z4xqji3fcvhl3jicekt4i4y2qm

Rigidity of group actions on solvable Lie groups

Burkhard Wilking
2000 Mathematische Annalen  
Clearly, 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.  ... 
doi:10.1007/s002089900091 fatcat:pkqp3nuqynhbdbbwcyrm6uuzt4

Summaries of articles published in this issue

1978 Czechoslovak Mathematical Journal  
In this paper 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.  ... 
doi:10.21136/cmj.1978.101523 fatcat:7lsfg3446nhmvor2bw7ge252ky
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