The main objects of this paper are the graded automorphisms of w x polytopal semigroup rings, i.e., semigroup rings k S where k is a field P Ž and S is the semigroup associated with a lattice polytope P Bruns, P w x. w x Gubeladze, and Trung BGT . The generators of k S correspond bijecP tively to the lattice points in P, and their relations are the binomials representing the affine dependencies...

The McKay–Navarro conjecture is a refinement of the McKay that additionally takes action some Galois automorphisms into account. We verify inductive condition in defining characteristic for finite groups Lie type with exceptional graph automorphisms, Suzuki and Ree groups, Bn(2) (n?2), non-generic Schur multiplier. This completes verification their characteristic.

We prove that the statement ‘For all Borel ideals I and J on ω, every isomorphism between Boolean algebras P(ω)/I and P(ω)/J has a continuous representation’ is relatively consistent with ZFC. In this model every isomorphism between P(ω)/I and any other quotient P(ω)/J over a Borel ideal is trivial for a number of Borel ideals I on ω. We can also assure that the dominating number, d, is equal t...

An automorphism σ of a simple finite dimensional complex Lie algebra g is called torsion, if σ has finite order in the group Aut(g) of all automorphisms of g. The torsion automorphisms of g were classified by Victor Kac in [12], as an application of his results on infinite dimensional Lie algebras. Those torsion automorphisms contained in the identity component G = Aut(g)◦ are called inner; the...

Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.

Abstract We describe the endomorphisms of direct product two free groups finite rank and obtain conditions for which subgroup fixed points is finitely generated, we do same periodic points. also automorphisms such a group solve three Whitehead problems automorphisms, monomorphisms in this class. an endomorphism to be uniformly continuous when suitable metric considered study infinite extension ...

The characterization of automorphisms of Bernstein algebras is an open problem. We only know some particular results. Previously we have characterized the automorphisms of quasiorthogonal, orthogonal, and strongly orthogonal weak Bernstein-Jordan algebras. In this paper we work on the minimal dimension with respect to quasiorthogonality, orthogonality, and strong orthogonality. We establish som...

We prove a compactness theorem for automorphisms of free groups. Namely, we show that the set of automorphisms keeping bounded the length of the uniform current is compact (up to conjugation.) This implies that the spectrum of the length of the images of the uniform current is discrete, answering to a conjecture of I. Kapovich.

In this work we introduce the concept of Generalized Atanassov’s Intuitionistic Fuzzy Index. We characterize it in terms of fuzzy implication operators and we propose a construction method with automorphisms. Finally, we study some special properties of the generalized Atanassov’s intuitionistic fuzzy index. Keywords— Atanassov’s Intuitionistic Fuzzy Index, Fuzzy Implication Operator, Automorph...

We show that the natural representation of SL 3 SL 5 SL 13 allows nonlinear equivariant automorphisms; more exactly, the group of polynomial au-tomorphisms on C 3 C 5 C 13 commuting with the simple SL 3 SL 5 SL 13-action is isomorphic to C n C. This is the rst example of a simple module with nonlinear equivariant automorphisms.