The Independence Theorem for the congruence lattice and the auto-morphism group of a nite lattice was proved by V. A. Baranski and A. Urquhart. Both proofs utilize the characterization theorem of congruence lattices of nite lattices (as nite distributive lattices) and the characterization theorem of auto-morphism groups of nite lattices (as nite groups). In this paper, we introduce a new, stron...

Abstract A rigid automorphism of a linking system is an that restricts to the identity on Sylow subgroup. inner conjugation by element in center At odd primes, it known each centric inner. We prove group outer automorphisms at prime $2$ elementary abelian and splits over subgroup automorphisms. In second result, we show if finite G for , then $p'$ -order modulo automorphisms, provided has no no...

A Cayley (di)graph Cay(G,S) of a group G is called normal if the right regular representation in full automorphism Cay(G,S), and CI-(di)graph for every Cay(G,T),Cay(G,S)≅Cay(G,T) implies that there σ∈Aut(G) such Sσ=T. We call an NDCI-group or NCI-group all digraphs graphs are CI-digraphs CI-graphs, respectively. prove cyclic order n only 8∤n, either = 8 8∤n.

It is shown that the complete Turing degrees do not form an automorphism base. A class A ⊆ the Turing degrees D is an automorphism base (see Lerman [1983]) if and only if any nontrivial automorphism of D necessarily moves at least one of its elements — or, equivalently, the global action of any such automorphism is completely determined by that on A . Jockusch and Posner [1981] demonstrated the...

Let S be a set of transpositions generating the symmetric group Sn, where n ≥ 3. It is shown that if the girth of the transposition graph of S is at least 5, then the automorphism group of the Cayley graph Cay(Sn, S) is the direct product Sn×Aut(T (S)), where T (S) is the transposition graph of S; the direct factors are the right regular representation of Sn and the image of the left regular ac...

We prove that IHSA, the theory of infinite dimensional Hilbert spaces equipped with a generic automorphism, is א0-stable up to perturbation of the automorphism, and admits prime models up to perturbation over any set. Similarly, APrA, the theory of atomless probability algebras equipped with a generic automorphism is א0-stable up to perturbation. However, not allowing perturbation it is not eve...

Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free group (free nilpotent group) must be very short. Dyer and Formanek [9] justified the conjecture concerning finitely generated free groups in the “sharpest sense” by proving that the automorphism group Aut(Fn) of a non-abelian free group Fn of finite rank n is complete. Recall that a group G is said to be ...

We show that the automorphism group of a divisible design D is isomorhic to a subgroup H of index 1 or 2 in the automorphism group Aut C(D) of the associated constant weight code. Only in very special cases, H is not the full automorphism group.

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of C0(R) ⊗ B(H) is an automorphism, respectively a surjective isometry.

A graph Γ is self-complementary if its complement is isomorphic to the graph itself. An isomorphism that maps Γ to its complement Γ is called a complementing isomorphism. The majority of this dissertation is intended to present my research results on the study of self-complementary vertex-transitive graphs. I will provide an introductory mini-course for the backgrounds, and then discuss four pr...