相关论文: Bounds for Finite Semiprimitive Permutation Groups…

A transitive permutation group is said to be semiprimitive if each of its normal subgroups is either semiregular or transitive.The class of semiprimitive groups properly contains primitive groups, quasiprimitive groups and innately…

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…

Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…

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…

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…

A transitive permutation group $G$ on a finite set $\Omega$ is said to be pre-primitive if every $G$-invariant partition of $\Omega$ is the orbit partition of a subgroup of $G$. It follows that pre-primitivity and quasiprimitivity are…

Let $G$ be a permutation group, and denote with $\mu(G)$ and $b(G)$ its minimal degree and base size respectively. We show that for every $\varepsilon>0$, there exists a transitive permutation group $G$ of degree $n$ with \[ \mu(G)b(G) \geq…

This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point…

We determine upper bounds for the maximum order of an element of a finite almost simple group with socle T in terms of the minimum index m(T) of a maximal subgroup of T: for T not an alternating group we prove that, with finitely many…

The subdegrees of a transitive permutation group are the orbit lengths of a point stabilizer. For a finite primitive permutation group which is not cyclic of prime order, the largest subdegree shares a non-trivial common factor with each…

A permutation group is called semiprimitive if each of its normal subgroups is either transitive or semiregular. Given nontrivial finite transitive permutation groups $L_1$ and $L_2$ with $L_1$ not semiprimitive, we construct an infinite…

We show that the minimal base size $b(G)$ of a finite primitive permutation group $G$ of degree $n$ is at most $2 (\log |G|/\log n) + 24$. This bound is asymptotically best possible since there exists a sequence of primitive permutation…

Working in a theory with an integer-valued dimension on interpretable sets, we classify pseudofinite definably primitive permutation groups acting on one-dimensional sets which satisfy a version of chain condition on centralizers and on…

General bounds are presented for the diameters of orbital graphs of finite affine primitive permutation groups. For example, it is proved that the orbital diameter of a finite affine primitive permutation group with a nontrivial point…

Recently, we have found a non-finitely based involution semigroup of order five. It is natural to question what is the smallest order of non-finitely based involution semigroups. It is known that every involution semigroup of order up to…

If $G$ is a group of permutations of a set $\Omega$ and $\alpha \in \Omega$, then the {\em $\alpha$-suborbits} of $G$ are the orbits of the stabilizer $G_\alpha$ on $\Omega$. The cardinality of an $\alpha$-suborbit is called a {\em…

The orbital diameter of a primitive permutation group is the maximal diameter of its orbital graphs. There has been a lot of interest in bounds for the orbital diameter. In this paper we provide explicit bounds on the diameters of groups of…

We study finite transitive permutation groups $G\leqslant\operatorname{Sym}(\Omega)$ such that all orbits of the conjugation action on $G$ of the normaliser of $G$ in $\operatorname{Sym}(\Omega)$ have size bounded by some constant. Our…

We classify minimal transitive subsemigroups of the finitary inverse symmetric semigroup modulo the classification of minimal transitive subgroups of finite symmetric groups; and semitransitive subsemigroups of the finite inverse symmetric…

A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in the context of automorphisms of graphs and occur naturally in…