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Transversals in Latin squares
R Montgomery - ar** of a group $ G $ is a bijection $\phi\colon G\to G $ such that $ x\mapsto
x\phi (x) $ is also bijective. Hall and Paige conjectured in 1955 that a finite group $ G $ has a …
x\phi (x) $ is also bijective. Hall and Paige conjectured in 1955 that a finite group $ G $ has a …
The geometry of diagonal groups
R Bailey, P Cameron, C Praeger… - Transactions of the …, 2022 - ams.org
Diagonal groups are one of the classes of finite primitive permutation groups occurring in the
conclusion of the O'Nan–Scott theorem. Several of the other classes have been described …
conclusion of the O'Nan–Scott theorem. Several of the other classes have been described …
An asymptotic for the Hall–Paige conjecture
Hall and Paige conjectured in 1955 that a finite group G has a complete map** if and only
if its Sylow 2-subgroups are trivial or noncyclic. This conjecture was proved in 2009 by …
if its Sylow 2-subgroups are trivial or noncyclic. This conjecture was proved in 2009 by …
Difference matrices with five rows over finite abelian groups
R Pan, RJR Abel, YA Bunjamin, T Feng… - Designs, Codes and …, 2022 - Springer
Let G be a finite group and k⩾ 2 be an integer. A (G, k, 1)-difference matrix (DM) is ak×| G|
matrix D=(d ij) with entries from G, such that for all distinct rows x and y, the multiset of …
matrix D=(d ij) with entries from G, such that for all distinct rows x and y, the multiset of …
Coset-wise affine functions and cycle types of complete map**s
A Bors, Q Wang - Finite Fields and Their Applications, 2022 - Elsevier
Let K be a finite field of characteristic p. We study a certain class of functions K→ K that
agree with an F p-affine function K→ K on each coset of a given additive subgroup W of K …
agree with an F p-affine function K→ K on each coset of a given additive subgroup W of K …
A note on a pair of orthogonal orthomorphisms of cyclic groups
M Zhang, T Feng, X Wang - Discrete Mathematics, 2023 - Elsevier
By giving previously unknown a pair of orthogonal orthomorphisms of cyclic groups of order
18 t+ 9 for any positive integer t, we complete the existence spectrum of a pair of orthogonal …
18 t+ 9 for any positive integer t, we complete the existence spectrum of a pair of orthogonal …
Totally -closed finite groups with trivial Fitting subgroup
A finite permutation group G≤ Sym (Ω) is called 2-closed if G is the largest subgroup of Sym
(Ω) which leaves invariant each of the G-orbits for the induced action on Ω× Ω. Introduced by …
(Ω) which leaves invariant each of the G-orbits for the induced action on Ω× Ω. Introduced by …
Spreading primitive groups of diagonal type do not exist
The synchronization hierarchy of finite permutation groups consists of classes of groups
lying between-transitive groups and primitive groups. This includes the class of spreading …
lying between-transitive groups and primitive groups. This includes the class of spreading …
Cycle type in Hall-Paige: A proof of the Friedlander-Gordon-Tannenbaum conjecture
A Müyesser - arxiv preprint arxiv:2303.16157, 2023 - arxiv.org
An orthomorphism of a finite group $ G $ is a bijection $\phi\colon G\to G $ such that $
g\mapsto g^{-1}\phi (g) $ is also a bijection. In 1981, Friedlander, Gordon, and Tannenbaum …
g\mapsto g^{-1}\phi (g) $ is also a bijection. In 1981, Friedlander, Gordon, and Tannenbaum …