Related papers: The Gelfand-Kazhdan criterion as a necessary and s…
We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand-Kazhdan criterion…
We establish conditions under which the fundamental group of a graph of finite $p$-groups is necessarily residually $p$-finite. The technique of proof is independent of previously established results of this type, and the result is also…
The Gelfand-Kazhdan criterion is a fundamental tool for studying multiplicity-one properties of local periods of representations. However, it does not apply to many cases arising in the relative Langlands program. Generalizing the usual…
A criterion for the HNN-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HNN-extension with arbitrary base group is proved.…
Let $G$ be a finite group. In this short note, we give a criterion of nilpotency of $G$ based on the existence of elements of certain order in each section of $G$.
We consider a set of necessary conditions which are efficient heuristics for deciding when a set of Wang tiles cannot tile a group. Piantadosi gave a necessary and sufficient condition for the existence of a valid tiling of any free group.…
In the paper we obtain an existence criterion for Hall subgroups of finite groups in terms of a composition series.
A necessary and sufficient compactness criterion in Schauder Spaces is proved.
We construct first examples of infinite groups having property (T) whose Kazhdan constants admit a lower bound independent of the choice of a finite generating set.
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…
We give a new equivalent condition for the Riemann hypothesis consisting in an order condition for certain finite rational combinations of the values of the Riemann zeta-function at even positive integers.
We establish a sufficient condition for a finitely generated pro-$p$ group to be accessible in terms of finite generation of the module of ends.
We prove a $p$-nilpotency criterion for finite groups in terms of the element orders of its $p'$-reduced sections that extends a nilpotency criterion by T{\u{a}}rn{\u{a}}uceanu.
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
In this paper, we will prove some sufficient conditions for the solvability of groups.
In the paper we obtain the existence criterion of a Carter subgroup in a finite group in terms of its normal series. An example showing that the criterion cannot be reformulated in terms of composition factors is given.
We obtain a necessary and sufficient condition for an algebraic set in a group to have a fully characteristic radical. As a result, we see that if the radical of a system of equation $S$ over a group $G$ is fully characteristic, then there…
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
We resolve Stillman's conjecture for families of polynomial rings that are graded by any semigroup under mild conditions. Conversely, we show that these conditions are necessary for the existence of a Stillman bound. This has applications…
Necessary and sufficient condition is given for a set $A\subset R^1$ to be a subset of the critical values set for a $C^k$ function $f:R^m \to R^1$.