Related papers: How close are pth powers in the Nottingham group?

Given a fixed integer n, we consider closed subgroups G of H = GL(n,Z_p) where Z_p denotes the ring of p-adic integers and p is sufficiently large in terms of n. Assuming that the Zariski closure of G has no toric part, we give a condition…

Let F be a finite field with q elements, let A be a finite dimensional F-algebra and let J=J(A) be the Jacobson radical of A. Then G=1+J is a p-group, where p is the characteristic of F. We refer to G as an F-algebra group. A subgroup H of…

Let $G$ be a graph and let $I := I (G)$ be its edge ideal. In this paper, we provide an upper bound of $n$ from which $\depth R/ I(G)^n$ is stationary, and compute this limit explicitly. This bound is always achieved if $G$ has no cycles of…

Let $G$ be a nilpotent-by-finite compact $p$-adic analytic group for some $p>2$, and $H = \mathbf{FN}_p(G)$ its finite-by-(nilpotent $p$-valuable) radical. Fix a finite field $k$ of characteristic $p$, and write $kG$ for the completed group…

This paper is concerned with the values of Harish-Chandra characters of a class of positive-depth, toral, very supercuspidal representations of $p$-adic symplectic and special orthogonal groups, near the identity element. We declare two…

We introduce the depth parameters of a finite semigroup, which measure how hard it is to produce an element in the minimum ideal when we consider generating sets satisfying some minimality conditions. We estimate such parameters for some…

We characterize finite $p$-groups $G$ of order up to $p^7$ for which the group of central automorphisms fixing the center element-wise is of minimum possibe order.

We present some results on character degree sums in connection with certain characteristics of finite groups such as p-solvability, solvability, supersolvability, and nilpotency. Some of them strengthen known results in the literature.

In this paper we introduce a new technique to study associated graded modules. Let $(A,\m)$ be a Noetherian local ring with $\depth A \geq 2$. Our techniques gives a necessary and sufficient condition for $\depth G_{\m^n}(A) \geq 2$ for all…

In this paper, we introduce the relative $n$-tensor nilpotent degree of a finite group $G$ with respect to a subgroup $H$ of $G$. The aim of this paper is to investigate this concept and give some results on this topic.

We show there exist representations of each maximal compact subgroup $K$ of the $p$-adic group $G=\mathrm{SL}(2,F)$, attached to each nilpotent coadjoint orbit, such that every irreducible representation of $G$, upon restriction to a…

Let $\pi$ be a set of primes containing $2$ and an odd prime $p$. It is proved that if a finite group $G$ has a Hall $\pi$-subgroup $H$, then the non-$p$-soluble length of $G$ is bounded above by the generalized Fitting height of $H$. The…

Some lower bounds of GK-dimension of Hopf algebras are given.

We show that an infinite group $G$ definable in a $1$-h-minimal field admits a strictly $K$-differentiable structure with respect to which $G$ is a (weak) Lie group, and show that definable local subgroups sharing the same Lie algebra have…

The subgroup commutativity degree of a group G has been defined in [6] as the probability that two subgroups of G commute, or equivalently that the product of two subgroups is again a subgroup. Problem 4.3 of [6] asks whether there exist…

For an odd prime $p$, we determine the lower central series of a large family of non-periodic GGS-groups, which has a density of roughly $(\frac{p-1}{p})^2$ within all GGS-groups. This means a significant extension of the knowledge…

Let $p$ be a prime and $q$ be a power of $p$. We compute the Chow ring of the classifying space of some Chevalley groups $G(\mathbb{F}_q)$, when considered as a finite algebraic group over a field of characteristic $p$ containing…

Let $H$ be a pointed Hopf algebra over an algebraically closed field of characteristic zero. If $H$ is a domain with finite Gelfand-Kirillov dimension greater than or equal to two, then $H$ contains a Hopf subalgebra of Gelfand-Kirillov…

Let G be a finite group, let p be a prime number, and let K be a field of characteristic 0 and k be a field of characteristic p, both large enough. In this note we state explicit formulae for the primitive idempotents of K\otimes pp_k(G),…

Let G be a finite group scheme over an algebraically closed field of positive characteristic. Assume further that the connected component of G is unipotent. It is shown that the projectivity of a rational G-module can be detected on a…