Solution. Since (ab)(abc) = (bc) and (abc)(ab) = (ac), it is easy to see that the center of S3 is the trivial subgroup. Therefore, the group of inner automorphisms of S3 is isomorphic to S3 and has size 6. On the other hand, S3 has 3 transpositions. These must be permuted by an automorphism of S3, and a nontrivial automorphism induces a nontrivial permutation. This gives an injective homomorphi...

It is known that Plotkin’s reduction theorem is very important for his theory of universal algebraic geometry [1, 2]. It turns out that this theorem can be generalized to arbitrary categories containing two special objects and in this case its proof becomes considerable more simple. This new proof and applications are the subject of the present paper. INTRODUCTION An automorphism φ of a categor...

Abstract: The left-right models provide an explanation for the parity asymmetry in the the Standard Model (SM). To further understand the origin of the left-right symmetry, we study a partial unification model based on SU(4)W×U(1)B−L which can be broken down to the minimal left-right model either through the Higgs mechanism in four dimensions or through the five-dimensional orbifold gauge symme...

Let $L_{m,c}$ stand for the free metabelian nilpotent Lie algebra of class $c$ rank $m$ over a field $K$ characteristic zero.
 Automorphisms form $\varphi(x_i)=e^{adu_i}(x_i)$ are called pointwise inner, where $e^{adu_i}$, is inner automorphism
 induced by element $u_i\in L_{m,c}$ each $i=1,\ldots,m$. In present study, we investigate group structure of
 $\text{\rm PInn}(L_{m,c})$...

Abstract We apply a method inspired by Popa's intertwining-by-bimodules technique to investigate inner conjugacy of MASAs in graph $C^*$ -algebras. First, we give new proof non-inner the diagonal MASA ${\mathcal {D}}_E$ its non-trivial image under quasi-free automorphism, where $E$ is finite transitive graph. Changing graphs representing algebras, this result applies some non automorphisms as w...

In this paper, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, show that usual inner automorphisms such quandles are precisely those “coherently extendible”. We then use result to compute global categories quandles, i.e. automorphism identity functors these categories.

We show that if a group automorphism of Cremona arbitrary rank is also homeomorphism with respect to either the Zariski or Euclidean topology, then it inner up field base-field. Moreover, we similar result holds consider groups polynomial automorphisms affine spaces instead groups.