Related papers: Demuskin groups with operators

Consider the Bianchi groups, namely the SL_2 groups over rings of imaginary quadratic integers. In the literature, there has been so far no example of p-torsion in the integral homology of the full Bianchi groups, for p a prime greater than…

We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin$^c$-Dirac operators, invariant under actions by possibly noncompact groups, with possibly noncompact orbit…

Let F be a finite group and X be a complex quasi-projective F-variety. For r in N, we consider the mixed Hodge-Deligne polynomials of quotients X^r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple…

Let $G$ be a transitive permutation group of degree $n$. We say that $G$ is $2'$-elusive if $n$ is divisible by an odd prime, but $G$ does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive…

Extending earlier work of Guralnick and of Cai and Zhang, we classify the almost simple groups which have transitive permutation representations of prime power degree $p^k$, and those which have $p$-complements (stabilisers of order coprime…

An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik-Chervonenkis density. Furthermore, strong abelian groups are…

The main purpose of this article is to study pro-$p$ groups with quadratic $\mathbb{F}_p$-cohomology algebra, i.e. $H^\bullet$-quadratic pro-$p$ groups. Prime examples of such groups are the maximal Galois pro-$p$ groups of fields…

Pro-$p$ groups of finite powerful class are studied. We prove that these are $p$-adic analytic, and further describe their structure when their powerful class is small. It is also shown that there are only finitely many finite $p$-groups of…

We classify indecomposable racks of order p^2 (p a prime). There are 2p^2 - 2p - 2 isomorphism classes, among which 2p^2 - 3p - 1 correspond to quandles. In particular, we prove that an indecomposable quandle of order p^2 is affine…

We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular,…

This paper explores some first-order properties of commuting-liftable pairs in pro-$\ell$ abelian-by-central Galois groups of fields. The main focus of the paper is to prove that minimized inertia and decomposition groups of many valuations…

Parafermions of order two and three are shown to be the fundamental tool to construct superspaces related to cubic and quartic extensions of the Poincar\'e algebra. The corresponding superfields are constructed, and some of their main…

In this paper we study the existence of free non-abelian subgroups in non-central permutable subgroups of general skew linear groups and locally finite group algebras.

The aim of this paper is to determine the non-abelian tensor square and Schur multiplier of groups of square free order and of groups of orders $p^2q$, $pq^2$ and $p^2qr$, where $p$, $q$ and $r$ are primes and $p<q<r$.

By a coprime commutator in a profinite group $G$ we mean any element of the form $[x, y]$, where $x,y\in G$ and $(|x|,|y|)=1$. It is well-known that the subgroup generated by the coprime commutators of $G$ is precisely the pronilpotent…

Given a principally polarized abelian variety $A$ of dimension $g$ over an algebraically closed field $k$ of characteristic $p$, the $p$ torsion $A[p]$ is a finite flat $p$-torsion group scheme of rank $p^{2g}$. There are exactly $2^g$…

We present a wide class of reflexive, precompact, non-compact, Abelian topological groups $G$ determined by three requirements. They must have the Baire property, satisfy the \textit{open refinement condition}, and contain no infinite…

We say that a finite group $G$ acting on a set $\Omega$ has Property $(*)_p$ for a prime $p$ if $P_\omega$ is a Sylow $p$-subgroup of $G_\omega$ for all $\omega\in\Omega$ and Sylow $p$-subgroups $P$ of $G$. Property $(*)_p$ arose in the…

We initiate the study of affine actions of groups on $\Lambda$-trees for a general ordered abelian group $\Lambda$; these are actions by dilations rather than isometries. This gives a common generalisation of isometric action on a…

Let a group $A$ act on the group $G$ coprimely. Suppose that the order of the fixed point subgroup $C_G(A)$ is not divisible by an arbitrary but fixed prime $p$. In the present paper we determine bounds for the $p$-length of the group $G$…