Related papers: Principal blocks for different primes, I
We use the theory of blocks of cyclic defect to prove that under a certain condition on the principal p-block of a finite group G the normalized unit group of the integral group ring of G contains an element of order pq if and only if so…
We determine the structure of 2-blocks with minimal nonabelian defect groups, by making use of the classification of finite simple groups.
This expository paper discusses some conjectures related to visibility and blockers for sets of points in the plane.
We begin by considering faithful matrix representations of elementary abelian groups in prime characteristic. The representations considered are seen to be determined up to change of bases by a single number. Studying this number leads to a…
We prove a logical implication between two old conjectures stated by Bapat and Sunder about the permanent of positive semidefinite matrices. Although Drury has recently disproved both conjectures, this logical implication yields a…
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…
In this note we generalise a method of Perott to give new proofs that there are infinitely many prime numbers.
This paper reviews recent results and open problems on the conductor of finite group characters, highlighting their connections to one another and to broader topics in the representation theory of finite groups.
We obtain the general k-correlations for a short divisor sum related to primes.
Recently, there has been substantial progress on the Alperin weight conjecture. As a step to establish the Alperin weight conjecture for all finite groups, we prove the inductive blockwise Alperin weight condition for simple groups of…
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank,…
We present new classes of permutation polynomials over finite fields.
Our main goal is to find a criterion to classify if a given group have a structure similar to a U(1) Lie group.
This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.
An elementary theory of strict $\infty $-categories with application to concrete duality is given. New examples of first and second order concrete duality are presented.
We develop the local-global theory of blocks for profinite groups. Given a field $k$ of characteristic $p$ and a profinite group $G$, one may express the completed group algebra $k[[G]]$ as a product $\prod_{i\in I}B_i$ of closed…
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
We describe first-degree prime ideals of biquadratic extensions in terms of first-degree prime ideals of two underlying quadratic fields. The identification of the prime divisors is given by numerical conditions involving their ideal norms.…
In this paper we give some basic results on blocking sets on minimum size for a finite chain geometry.