Related papers: A cohomological property of semi-abelian $p$-group…

We describe a general setting for the definition of semi-infinite cohomology of finite dimensional algebras, and provide its categorical interpretation. We apply this interpretation to compute semi-infinite cohomology of some modules over…

We first introduce global arithmetic cohomology groups for quasi-coherent sheaves on arithmetic varieties, adopting an adelic approach. Then, we establish fundamental properties, such as topological duality and inductive long exact…

We completely characterize by finding necessary and sufficient conditions those co-Bassian and generalized co-Bassian Abelian groups having, respectively, the hereditary or the super property, thus giving a new insight in the full discovery…

The equivariant cohomology for actions of compact connected abelian groups and elementary abelian p-groups have been widely studied in the last decades. We study some of these results on actions of finite cyclic groups over a field of…

We prove that no quantifier-free formula in the language of group theory can define the $\aleph_1$-half graph in a Polish group, thus generalising some results from [6]. We then pose some questions on the space of groups of automorphisms of…

The aim of the paper is to give a full classification of factorizations of groups in terms of descent cohomology (pointed) sets introduced in [5]. We show that descent cohomology includes Serre's non-abelian group cohomology as a special…

Recently, the concept of the $p$-numerical semigroup with $p$-symmetric properties has been introduced. When $p=0$, the classical numerical semigroup with symmetric properties is recovered. In this paper, we further study the $p$-numerical…

Let $G$ be a finite non-cyclic $p$-group of order at least $p^3$. If $G$ has an abelian maximal subgroup, or if $G$ has an elementary abelian centre with $C_G(Z(\Phi(G))) \ne \Phi(G)$, then $|G|$ divides $|\text{Aut}(G)|$.

It is shown that if G is a finite p-group of coclass 2 with p > 2, then G has a noninner automorphism of order p.

We determine all finite p-groups that admit a faithful, self-similar action on the p-ary rooted tree such that the first level stabilizer is abelian. A group is in this class if and only if it is a split extension of an elementary abelian…

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman…

We study a class of finite groups $G$ which behave similarly to elementary abelian $p$-groups with $p$ prime, that is, there exists a subgroup $N$ such that all elements of $G\setminus N$ are conjugate or inverse-conjugate under $\Aut(G)$.…

We give an infinite family of non-abelian strongly real Beauville $p$-groups for any odd prime $p$ by considering the lower central quotients of the free product of two cyclic groups of order $p$. This is the first known infinite family of…

We extend the notion of a partial cohomology group $H^n(G,A)$ to the case of non-unital $A$ and find interpretations of $H^1(G,A)$ and $H^2(G,A)$ in the theory of extensions of semilattices of abelian groups by groups.

We prove analogues of the major algebraic results of Greenberg-Vatsal for Selmer groups of $p$-ordinary newforms over $\mathbf{Z}_p$-extensions which may be neither cyclotomic nor anticyclotomic, under a number of technical hypotheses,…

We prove that the degree $r(2p-3)$ cohomology of any finite group of Lie type over $\mathbb{F}_{p^r}$, with coefficients in characteristic $p$, is nonzero as long as its Coxeter number is at most $p$. We do this by providing a simple…

We give a proof of the finite generation of the cohomology ring of a finite p-group over F_p by reduction to the case of elementary abelian groups, based on Serre's Theorem on products of Bocksteins.

We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P.M. Soltan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we…

Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic space group of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or…

We establish lower bounds for the $p$-divisibility of the quantity $\#\operatorname{Hom}(G,GL_n(\mathbb{F}_q))$, the number of homomorphisms from $G$ to a general linear group, where $G$ is an Abelian $p$-group. This is in analogy to the…