Add to ORKGLet $G$ be a finite group, let $H$ be a core-free subgroup and let $b(G,H)$ denote the base size for the action of $G$ on $G/H$. Let $\alpha(G)$ be the number of conjugacy classes of core-free subgroups $H$ of $G$ with $b(G,H) \geqslant 3$. We say that $G$ is a strongly base-two group if $\alpha(G) \leqslant 1$, which means that almost every faithful transitive permutation representation of $G$ has base size $2$. In this paper we study the strongly base-two finite groups with trivial Frattini subgroup.Comment: 22 page
A group $G$ is integrable if it is isomorphic to the derived subgroup of a group $H$; that is, if $H...
In this thesis we consider base size and properties of the generating graph for finite groups. L...
In this paper, we compute the essential l-dimension of the finite groups of classical Lie type for l...
The greatest power of a prime $p$ dividing the natural number $n$ will bedenoted by $n_p$. Let $Ind_...
Let $G$ be a permutation group on a finite set $\Omega$. The base size of $G$ is the minimal size of...
We present a characterization of the finite groups in which all real classes have prime powers size....
summary:Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$-conjugacy ...
AbstractA base B for a finite permutation group G acting on a set Ω is a subset of Ω with the proper...
Given two positive integers $n$ and $k$, we obtain a formula for the base size of the symmetric grou...
Bridging the work of Cameron, Harary, and others, we examine the base size set B(G) and determining ...
We establish a new connection between local and large-scale structure in compactly generated totally...
Let $G$ be a finite permutation group on $\Omega$. An ordered sequence $(\omega_1,\ldots,\omega_\ell...
We study a family of finitely generated residually finite small cancellation groups. These groups ar...
We show that the minimal base size $b(G)$ of a finite primitive permutation group $G$ of degree $n$ ...
Let $\Gamma$ be a finite group, let $\theta$ be an involution of $\Gamma$, and let $\rho$ be an irre...
A group $G$ is integrable if it is isomorphic to the derived subgroup of a group $H$; that is, if $H...
In this thesis we consider base size and properties of the generating graph for finite groups. L...
In this paper, we compute the essential l-dimension of the finite groups of classical Lie type for l...
The greatest power of a prime $p$ dividing the natural number $n$ will bedenoted by $n_p$. Let $Ind_...
Let $G$ be a permutation group on a finite set $\Omega$. The base size of $G$ is the minimal size of...
We present a characterization of the finite groups in which all real classes have prime powers size....
summary:Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$-conjugacy ...
AbstractA base B for a finite permutation group G acting on a set Ω is a subset of Ω with the proper...
Given two positive integers $n$ and $k$, we obtain a formula for the base size of the symmetric grou...
Bridging the work of Cameron, Harary, and others, we examine the base size set B(G) and determining ...
We establish a new connection between local and large-scale structure in compactly generated totally...
Let $G$ be a finite permutation group on $\Omega$. An ordered sequence $(\omega_1,\ldots,\omega_\ell...
We study a family of finitely generated residually finite small cancellation groups. These groups ar...
We show that the minimal base size $b(G)$ of a finite primitive permutation group $G$ of degree $n$ ...
Let $\Gamma$ be a finite group, let $\theta$ be an involution of $\Gamma$, and let $\rho$ be an irre...
A group $G$ is integrable if it is isomorphic to the derived subgroup of a group $H$; that is, if $H...
In this thesis we consider base size and properties of the generating graph for finite groups. L...
In this paper, we compute the essential l-dimension of the finite groups of classical Lie type for l...