A shift automorphism algebra is one satisfying the conditions of the shift automorphism theorem, and a shift automorphism variety is a variety generated by a shift automorphism algebra. In this paper, we show that every shift automorphism variety contains a countably infinite subdirectly irreducible algebra. 2000 Mathematics subject classification: primary 03C05; secondary 08B05, 08B26.

We consider homogeneous varieties of linear algebras over an associative-commutative ring K with 1, i.e., the varieties in which free algebras are graded. Let F = F (x1, ..., xn) be a free algebra of some variety Θ of linear algebras over K freely generated by a set X = {x1, ..., xn}, EndF be the semigroup of endomorphisms of F , and Aut EndF be the group of automorphisms of the semigroup EndF ...

This note gives an elementary proof that the symmetric groups possess only one exceptional symmetry. I am referring to the fact that the outer automorphism group of the symmetric group Symn is trivial unless n = 6 and the outer automorphism group of Sym6 has a unique nontrivial element. When we study symmetric groups, we often invoke their natural faithful representation as permutations of a se...

On the Automorphism Tower of Free Nilpotent Groups Martin Dimitrov Kassabov 2003 In this thesis I study the automorphism tower of free nilpo-tent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the discrete group can be embedded into the automorphism group of the Lie group. Th...

IN a previous article,* devoted to a study of conjugate operators, attention was called to the fact that a complete set of conjugate operators which are not all relatively commutative is transformed under the group according to a substitution group which is at most triply transitive. It is easy to prove that this substitution group is at most doubly transitive, and, as the p conjugates of order...

The concept of graph symmetry is explained in terms of the vertex automorphism group, which is a subgroup of the complete vertex permutation group. The automorphism group can be deduced from the automorphism partition of graph vertices. An algorithm is described which constructs the automorphism group of a graph from the automorphism vertex partitioning. The algorithm is useful especially for g...

The hull of a linear code C is the intersection with its dual C⊥, where often defined respect to Euclidean or Hermitian inner product. low dimensions gets much interest due crucial role in determining complexity algorithms for computing automorphism group and checking permutation equivalence two codes. Recently, both hulls have found another application quantum error correcting codes entangleme...

Automorphism groupS of Hadamard matrices are related to automorphism groups of de.Jigns, and the automorphism groups of the Paley-Hadamard matrices are determined .