Related papers: On hereditarily self-similar $p$-adic analytic pro…

The aim of this paper is to develop the theory of groups definable in the $p$-adic field ${\mathbb Q}_p$, with ``definable $f$-generics" in the sense of an ambient saturated elementary extension of ${\mathbb Q}_p$. We call such groups…

We study the structure of the category of graded, connected, countable-dimensional, commutative and cocommutative Hopf algebras over a perfect field $k$ of characteristic $p$. Every $p$-torsion object in this category is uniquely a direct…

Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam-Liu-Sharifi-Wake-Wang. We prove that the pro-p completion of the right-angled Artin group associated to a chordal simplicial graph is of p-absolute Galois…

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 $\Aut(G)$.…

Let $f$ be an irreducible polynomial of prime degree $p\geq 5$ over $\QQ$, with precisely $k$ pairs of complex roots. Using a result of Jens H\"{o}chsmann (1999), we show that if $p\geq 4k+1$ then $\Gal(f/\QQ)$ is isomorphic to $A_{p}$ or…

In this paper we investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a…

It is shown that the Zassenhaus restricted $\mathbb F_p$-Lie algebra of a (pro-p) group G can be presented by the Magnus Lie algebra of G. For the class of (pro-p) groups for which the terms of the lower central series are torsion-free, the…

Profinite groups with a cyclotomic $p$-orientation are introduced and studied. The special interest in this class of groups arises from the fact that any absolute Galois group $G_{K}$ of a field $K$ is indeed a profinite group with a…

In this paper we introduce a new method for finding Galois groups by computer. This is particularly effective in the case of Galois groups of p-extensions ramified at finitely many primes but unramified at the primes above p. Such Galois…

A self-similar group of finite type is the profinite group of all automorphisms of a regular rooted tree that locally around every vertex act as elements of a given finite group of allowed actions. We provide criteria for determining when a…

For any odd prime $p$ and any imaginary quadratic field $K$, the $p$-tower group $G_K$ associated to $K$ is the Galois group over $K$ of the maximal unramified pro-$p$-extension of $K$. This group comes with an action of a finite group…

We prove that groups that are mod-p-homology equivalent are isomorphic modulo any term of their derived p-series, in precise analogy to Stallings' 1963 result for the lower-central p-series. Similarly spaces that are mod-p-homology…

In [10] Benjamin Klopsch and Ilir Snopce posted the conjecture that for $p\geq 3$ and $G$ a torsion-free pro-$p$ group $d(G)=\dim (G)$ is a sufficient and necessary condition for the pro-$p$ group $G$ to be uniform. They pointed out that…

For $G$ a symplectic or orthogonal $p$-adic group (not necessarily split), or an inner form of a general linear $p$-adic group, we compute the endomorphism algebras of some induced projective generators \`a la Bernstein of the category of…

We disprove a well-known conjecture of Boston (2000), which claims that a just-infinite pro-$p$ group is branch if and only if it admits a positive-dimensional embedding in the group of $p$-adic automorphisms. This is obtained as a result…

Let $X$ be a proper, smooth, and geometrically connected curve of genus $g(X)\ge 1$ over a $p$-adic local field. We prove that there exists an effectively computable open affine subscheme $U\subset X$ with the property that $period (X)=1$,…

We define the notion of accessibility for a pro-$p$ group. We prove that finitely generated pro-$p$ groups are accessible given a bound on the size of their finite subgroups. We then construct a finitely generated inaccessible pro-$p$…

Let $X$ be a smooth projective connected curve of genus $g\ge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show…

We prove that torsion in the abelianizations of open normal subgroups in finitely presented pro-$p$ groups can grow arbitrarily fast. By way of contrast in $\mathbb Z_p$- analytic groups the torsion growth is at most polynomial.

It is known that a finite group G can only act freely on affine n-space if K has positive characteristic p and G is a p-group. In that case the group action is "non-linear" and the ring of regular functions must be a trace-surjective…