Results 111 to 120 of about 176,865 (291)
Cyclotomy and difference families in elementary abelian groups
Journal of Number Theory, 1972 AbstractBy a (v, k, λ)-difference family in an additive abelian group G of order v, we mean a family (Bi ∣ i ∈ I) of subsets of G, each of cardinality k, and such that among the differences (a − b ∣ a, b ∈ Bi; a ≠ b; i ∈ I) each nonzero g ∈ G occurs λ times. The existence of such a difference family implies the existence of a (v, k, λ)-BIBD with G as a
openaire +2 more sources
Commuting Pairs in Quasigroups
Journal of Combinatorial Designs, Volume 33, Issue 11, Page 418-427, November 2025.ABSTRACT A quasigroup is a pair ( Q , ∗ ), where Q is a nonempty set and ∗ is a binary operation on Q such that for every ( a , b ) ∈ Q 2, there exists a unique ( x , y ) ∈ Q 2 such that a ∗ x = b = y ∗ a. Let ( Q , ∗ ) be a quasigroup. A pair ( x , y ) ∈ Q 2 is a commuting pair of ( Q , ∗ ) if x ∗ y = y ∗ x.
Jack Allsop, Ian M. Wanless
wiley +1 more source
Set Reconstruction on the Hypercube
Discrete Analysis, 2017 Set reconstruction on the hypercube, Discrete Analysis 2017:17, 10 pp. A well-known open problem in graph theory that goes back to the late 1950s is the so-called _reconstruction conjecture_.
Luke Pebody
doaj +1 more source
The third cohomology group classifies crossed module extensions
, 2009 We give an elementary proof of the well-known fact that the third cohomology group H^3(G, M) of a group G with coefficients in an abelian G-module M is in bijection to the set Ext^2(G, M) of equivalence classes of crossed module extensions of G with M ...
Thomas, Sebastian
core
On 3‐Designs From P G L ( 2 , q )
Journal of Combinatorial Designs, Volume 33, Issue 11, Page 428-432, November 2025.ABSTRACT The group P G L ( 2 , q ) acts 3‐transitively on the projective line G F ( q ) ∪ { ∞ }. Thus, an orbit of its action on the k‐subsets of the projective line is the block set of a 3‐ ( q + 1 , k , λ ) design. We find the parameters of the designs formed by the orbit of a block of the form 〈 θ r 〉 or 〈 θ r 〉 ∪ { 0 }, where θ is a primitive ...
Paul Tricot
wiley +1 more source
Elementary Abelian $p$ Subgroups of Lie Groups
Publications of the Research Institute for Mathematical Sciences, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dietrich Notbohm, Richard Kane
openaire +2 more sources
Communications on Pure and Applied Mathematics, Volume 78, Issue 10, Page 2001-2118, October 2025.Abstract We analyse and clarify the finite‐size scaling of the weakly‐coupled hierarchical n$n$‐component |φ|4$|\varphi |^4$ model for all integers n≥1$n \ge 1$ in all dimensions d≥4$d\ge 4$, for both free and periodic boundary conditions. For d>4$d>4$, we prove that for a volume of size Rd$R^{d}$ with periodic boundary conditions the infinite‐volume ...
Emmanuel Michta +2 more
wiley +1 more source
On Endomorphism Universality of Sparse Graph Classes
Journal of Graph Theory, Volume 110, Issue 2, Page 223-244, October 2025.ABSTRACT We show that every commutative idempotent monoid (a.k.a. lattice) is the endomorphism monoid of a subcubic graph. This solves a problem of Babai and Pultr and the degree bound is best‐possible. On the other hand, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids. As a by‐product,
Kolja Knauer, Gil Puig i Surroca
wiley +1 more source
A Sufficient Condition for Solvability in Groups Admitting Elementary Abelian Operator Groups [PDF]
, 1977 Martin R. Pettet
openalex +1 more source
On Bipartite Biregular Large Graphs Derived From Difference Sets
Journal of Graph Theory, Volume 110, Issue 2, Page 174-181, October 2025.ABSTRACT A bipartite graph G = ( V , E ) with V = V 1 ∪ V 2 is biregular if all the vertices of each stable set, V 1 and V 2, have the same degree, r and s, respectively. This paper studies difference sets derived from both Abelian and non‐Abelian groups.
Gabriela Araujo‐Pardo +3 more
wiley +1 more source