Related papers: Identity theorem for pro-$p$-groups

We attempt to generalize the $p$-modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our tasks through modules of transporter category algebras, a type…

We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.

Let $R$ be a finite unital commutative ring. We introduce a new class of finite groups, which we call hereditary groups over $R$. Our main result states that if $G$ is a hereditary group over $R$ then a unital algebra isomorphism between…

I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is governed by the possibility of collapse: elements may be…

To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…

We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the normaliser and centraliser structure of these. For toral…

By counting the numbers of periodic points of all periods for some interval maps, we obtain infinitely many new congruence identities in number theory.

We study the representation theory of the symmetric group $S_n$ in positive characteristic $p$. Using features of the LLT-algorithm we give a conjectural description of the projective cover $P(\lambda)$ of the simple module $D(\lambda)$…

Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…

The main result of [4] is that all finitely presented groups of p-deficiency greater than one are p-large. Here we prove that groups with a finite presentation of p-deficiency one possess a finite index subgroup that surjects onto . This…

Let $R$ be a commutative ring with identity. For an $R$-module $M$, the notion of strongly prime submodule of $M$ is defined. It is shown that this notion of prime submodule inherits most of the essential properties of the usual notion of…

A conjecture of Berkovich asserts that every non-simple finite p-group has a non-inner automorphism of order p. This conjecture is far from being proved despite the great effort devoted to it. In this paper we prove it for p-groups of…

In the theory of unitary group representations, a group is called type I if all factor representations are of type I, and by a celebrated theorem of James Glimm [Gli61b], the type I groups are precisely those groups for which the…

We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.

Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…

We consider the generalized character $\Psi_{1,p,G}$ of a finite group $G$ which vanishes on all $p$-singular elements of $G$ and whose value at each $p$-regular $y \in G$ is the number of $p$-elements of $C_{G}(y)$. We conjecture that this…

This paper presents both a proof method and a result. The proof method presented is particularly suitable for uniformly proving families of identities satisfied by a family of recursive sequences. To illustrate the method, we study the…

We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.

Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.

We define a simple dependent type theory and prove that its well-formed types correspond exactly to finite inverse categories.