We discuss the group of automorphisms of a general MR-algebra. We develop several functors between implication algebras and cubic algebras. These allow us to generalize the notion of inner automorphism. We then show that this group is always isomorphic to the group of inner automorphisms of a filter algebra.

The structure of block-spin embeddings of the U(1) lattice current algebra is described. For an odd number of lattice sites, the inner realizations of the shift automorphism are classified. We present a particular inner shift operator which admits a factorization involving quantum dilogarithms analogous to the results of Faddeev and Volkov.

In this paper, we prove that the full automorphism group of the derangement graph Γn (n ≥ 3) is equal to (R(Sn) ⋊ Inn(Sn)) ⋊ Z2, where R(Sn) and Inn(Sn) are the right regular representation and the inner automorphism group of Sn respectively, and Z2 = 〈φ〉 with the mapping φ : σ φ = σ−1, ∀σ ∈ Sn. Moreover, all orbits on the edge set of Γn (n ≥ 3) are determined.

Theorem (1) There is an involution C of G satisfying: C(h) = h −1 (h ∈ H); (2) C(g) ∼ g −1 for all semisimple elements g; (3) Any two such involutions are conjugate by an inner automorphism;

Let A be a separable unital C-algebra. It is shown that A is type I if and only if the CNT-entropy of every inner automorphism of A is zero.

An A-loop is a loop in which every inner mapping is an automorphism. A problem which had been open since 1956 is settled by showing that every diassociative A-loop is Moufang.

1. Introduction. In this paper, we study the fixed point sets and stable subgroups of automorphisms of a connected algebraic linear group over an algebraically closed field of arbitrary characteristic. [7] contains a description of most of the results of this paper, and some material in [7] is essential for the present paper. Many of the results discussed in the present paper were proved at cha...

This research was motivated by universal algebraic geometry. One of the central questions of universal algebraic geometry is: when two algebras have the same algebraic geometry? For answer of this question (see [8],[10]) we must consider the variety Θ, to which our algebras belongs, the category Θ of all finitely generated free algebras of Θ and research how the group AutΘ of all the automorphi...

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 ...