Related papers: Some special coprime actions and their consequence

In this paper we measure how efficiently a finite simple group $G$ is generated by its elements of order $p$, where $p$ is a fixed prime. This measure, known as the $p$-width of $G$, is the minimal $k\in \mathbb{N}$ such that any $g\in G$…

We study actions of discrete groups on contractible topological spaces in which either (1) all stabilizers lie in the family of subgroups of prime power order or (2) all stabilizers lie in the family of finite subgroups. We compare the…

It is proved that if a finite $p$-soluble group $G$ admits an automorphism $\varphi$ of order $p^n$ having at most $m$ fixed points on every $\varphi$-invariant elementary abelian $p'$-section of $G$, then the $p$-length of $G$ is bounded…

Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if $C_G(N) \leq N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing…

In this paper, we investigate the structure of finite group G by assuming that the intersections between p-sylowizers of some p-subgroups of G and $O^p(G)$ are S-permutable in G. We obtain some criterions for p-nilpotency of a finite group.

Consider a finite l-group acting on the affine space of dimension n over a field k, whose characteristic differs from l. We prove the existence of a fixed point, rational over k, in the following cases: --- The field k is p-special for some…

We are investigating the lifting problem for local actions involving semidirect products of a cyclic $p$-group with a cyclic group prime to $p$, where $p$ represents the characteristic of the special fiber. We establish a criterion based on…

Given a $p$-adic group $G$ equipped with an action of a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$, and a reductive fixed-point subgroup $G^\Gamma$, we establish a relationship between constructions of types for these two groups…

For a prime number $p$, we give a new restriction on pro-$p$ groups $G$ which are realizable as the maximal pro-$p$ Galois group $G_F(p)$ for a field $F$ containing a root of unity of order $p$. This restriction arises from Kummer Theory…

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first…

We classify the finite groups with the property that any two different character codegrees are coprime. In general, we conjecture that if $k$ is a positive integer such that for any prime $p$ the number of character codegrees of a finite…

Let $G$ be a finite $p$-solvable group, where $p$ is an odd prime. We establish a connection between extendible irreducible characters of subgroups of $G$ that lie under monomial characters of $G$ and nilpotent subgroups of $G$. We also…

We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact…

We consider fully effective orientation-preserving smooth actions of a given finite group G on smooth, closed, oriented 3-manifolds M. We investigate the relations that necessarily hold between the numbers of fixed points of various…

In this paper, we address the following question: when is a finite $p$-group $G$ self-similar, i.e. when can $G$ be faithfully represented as a self-similar group of automorphisms of the $p$-adic tree? We show that, if $G$ is a self-similar…

We present a classification of finite $p$-groups $G$ with $\gamma_2(G)$, the commutator subgroup of $G$, of order $p^4$ and exponent $p$ such that not all elements of $\gamma_2(G)$ are commutators.

Any non-abelian finite $p$-group has a non-inner automorphism of order $p$.

In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…

Fixed point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime $p$ and a finite group $G$, we use fixed point ratios…