Related papers: Some infinite permutation groups and related finit…

A base of a permutation group (X,G) is a subset B of X such that its pointwise stabilizer is the trivial group. A list (x1,x2, ... ,xk) of elements of X is irredundant if each element is not in the pointwise stabilizer of its predecessors.…

We prove that there exists a universal constant $c$ such that any finite primitive permutation group of degree $n$ with a non-trivial point stabilizer is a product of no more than $c\log n$ point stabilizers.

Let $G$ be a transitive permutation group on a finite set of size at least $2$. By a well known theorem of Fein, Kantor and Schacher, $G$ contains a derangement of prime power order. In this paper, we study the finite primitive permutation…

Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.

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.

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This…

In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…

We give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers. This gives further insight into the structure lattices of branch groups introduced by the second author.…

We investigate stabilizers of finite sets of rational points in Cantor space for the Higman-Thompson groups $V_{n,r}$. We prove that the pointwise stabilizer is an iterated ascending HNN extension of $V_{n,q}$ for any $q\geq 1$. We also…

We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…

All finite sets of equiangular lines spanning finite-dimensional unitary spaces are determined for which the action on the lines of the set-stabilizer in the unitary group is 2-transitive with a regular normal subgroup.

Let $\sigma=\{\sigma_{i}|i\in I\}$ be a partition of the set of all primes $\mathbb{P}$, $G$ a finite group and $\sigma(G)=\{\sigma_{i}|\sigma_{i}\cap \pi(|G|)\neq\emptyset\}$. A subgroup $S$ of a group $G$ is called a $\sigma_i$-sylowizer…

This is the second of two papers treating faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties; in the first paper we considered the module itself and its projective space, while…

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it…

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…

Let $H$ be a subgroup of a group $G$. The permutizer $P_G(H)$ is the subgroup generated by all cyclic subgroups of $G$ which permute with $H$. A subgroup $H$ of a group $G$ is strongly permutable in $G$ if $P_U(H)=U$ for every subgroup $U$…

We investigate properties of finite transitive permutation groups $(G, \Omega)$ in which all proper subgroups of $G$ act intransitively on $\Omega.$ In particular, we are interested in reduction theorems for minimally transitive…

The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…

A subgroup of a finite group G is said to be second maximal if it is maximal in every maximal subgroup of G that contains it. A question which has received considerable attention asks: can every positive integer occur as the number of the…