We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite ordered structures with finitely many partial equivalence relations with convex classes.

The two parts of this paper consider combinatorial and geometric aspects of semibent functions. In the first part of this note we obtain 2– designs from semibent functions and we characterize their automorphism groups. In the second part semibent functions of partial spread type with a linear structure are investigated.

a longstanding conjecture asserts that every finite nonabelian $p$-group admits a noninner automorphism of order $p$‎. ‎let $g$ be a finite nonabelian $p$-group‎. ‎it is known that if $g$ is regular or of nilpotency class $2$ or the commutator subgroup of $g$ is cyclic‎, ‎or $g/z(g)$ is powerful‎, ‎then $g$ has a noninner automorphism of order $p$ leaving either the center $z(g)$ or the frattin...

a longstanding conjecture asserts that every finite nonabelian $p$-group admits a noninner automorphism of order $p$. let $g$ be a finite nonabelian $p$-group. it is known that if $g$ is regular or of nilpotency class $2$ or the commutator subgroup of $g$ is cyclic, or $g/z(g)$ is powerful, then $g$ has a noninner automorphism of order $p$ leaving either the center $z(g)$ or the frattini subgro...

are not. (In the second example, the two sets can be mapped to each other by a partial automorphism, but not by one that extends to a automorphism of the real numbers.) Here is the definition of FM sets. The definition is parametrized by a set of atoms. The atoms are given as a relational structure, which induces a notion of automorphism. (One can also consider atoms with function symbols, but ...

We show: There are pairs of universes V1 ⊆ V2 and there is a notion of forcing P ∈ V1 such that the change mentioned in the title occurs when going from V1[G] to V2[G] for a P -generic filter G over V2. We use forcing iterations with partial memories. Moreover, we implement highly transitive automorphism groups into the forcing orders.

A spread is a set of lines of PG(d, q), which partition the point set. A parallelism is a partition of the set of lines by spreads. Some constructions of constant dimension codes that contain lifted MRD codes are based on parallelisms of projective spaces. A parallelism is transitive if it has an automorphism group which is transitive on the spreads. A parallelism is point-transitive if it has ...

In some recent papers the method of partial differences introduced by the author in [4] was very helpful in the construction of cyclic cycle systems. Here we use and describe in all details this method for the more general purpose of constructing cycle decompositions with a sharply vertex transitive automorphism group not necessarily cyclic.

in this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. with this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. n(g) and s(g) are the set of all nilpotency classes and the set of all solvability classes for the group g with respect to different automorphi...