Related papers: Principal blocks for different primes, I

We prove that for all $n$, simultaneously, we can choose prime filtrations of $R/I^n$ such that the set of primes appearing in these filtrations is finite.

In this paper, using the well known fact that the series of reciprocals of primes diverges, we obtain a general inequality for gaps of consecutive primes that holds for infinitely many primes. As it is shown the key ingredient for this…

Building on previous work by Caicedo and the second author, we develop a method that decides the existence of units of finite order in blocks of $\mathbb{Z}_p G$ of defect 1. This allows us to prove that if $p$ is a prime and $G$ is a…

In this paper, we prove a few lemmas concerning Fibonacci numbers modulo primes and provide a few statements that are equivalent to Wall-Sun-Sun Prime Conjecture. Further, we investigate the conjecture through heuristic arguments and…

In this note, we investigate how different fundamental groups of presentations of a fixed algebra $A$ can be. For finitely many finitely presented groups $G_i$, we construct an algebra $A$ such that all $G_i$ appear as fundamental groups of…

We discuss the relationship among various conjectures in the minimal model theory including the finite generation conjecture of the log canonical rings and the abundance conjecture. In particular, we show that the finite generation…

We show the existence of infinitely many prime knots each of which having in their complements meridional essential surfaces with two boundary components and arbitrarily high genus.

The Malle-Navarro conjecture relates central block theoretic invariants in two inequalities. In this paper, we prove the conjecture for the 2-blocks and the unipotent 3-blocks of the general linear and unitary groups in non-defining…

In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.

We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.

Many of the conjectures of current interest in the representation theory of finite groups in characteristic $p$ are local-to-global statements, in that they predict consequences for the representations of a finite group $G$ given data about…

We present a new, elementary, dynamical proof of the prime number theorem.

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

This note highlights an interesting connection between Euler sums of even weight and prime numbers.

We prove a conjecture on Rubin-Stark elements, which was recently proposed by the author, and also by Mazur and Rubin, in a special case.

We give a more strong heuristic justification of our conjecture on the excess of the odious primes.

In this short note, we prove a formula for the group inverse of a block matrix and consider the pseudo principal pivot transform expressed in terms of group inverses. Extensions of the usual principal pivot transform, where the usual…

Using the Rowland idea, we find two infinite sets of generators of primes. We also pose some conjectures concerning twin primes.

We give new evidences to the fact that the structure of a solvable group can be controlled by irreducible monomial characters. In particular we inspect the role of monomial characters in Isaacs-Navarro-Wolf's conjecture and in Gluck's…

We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…