Automorphisms of the Gersten Group

Siberian Mathematical Journal - The Gersten group $ G $ is the split extension $ F_{3}rtimes_{varphi}{??} $ of the free group $ F_{3} $ with basis $ {a,b,c} $ by the automorphism...     

Automorphisms of the Hatcher-Thurston complex

Let S be a compact, connected, orientable surface of positive genus. Let be the Hatcher-Thurston complex of S. We prove that Aut is isomorphic to the extended mapping class group of S modulo its center. The first author is supported by a Rackham Faculty Fellowship, Horace H. Rackham School of Graduate Studies, University of Michigan. The second author is supported in part by the Turkish Academy of Sciences under the Young Scientists Award Program (MK/TüBA-GEBİP 2003-10).     

Automorphisms of groups

The survey presents classical assertions due to Nielsen, Whitehead, and others, well-known theorems on automorphisms included in monographs on group theory, and recent results in this area. Attention is focused on the progress in automorphism groups theory for free, solvable, modular, and profinite groups. New tools of investigation using graphs and geometrical ideas are also discussed.     

Lifting Automorphisms

Let A be a unital nuclear separable C*-algebra which satisfies the Universal Coefficient Theorem and E be a unital essential extension of the form:

Central Automorphisms and Inner Automorphisms in Finitely Generated Groups

Let G be a group and Aut_c(G) be the group of all central automorphisms of G. We know that in a finite p-group G, Aut_c(G) = Inn(G) if and only if Z(G) = G′ and Z(G) is cyclic. But we shown that we cannot extend this result for infinite groups. In fact, there exist finitely generated nilpotent groups of class 2 in which G′ =Z(G) is infinite cyclic and Inn(G) < C* = Aut_c(G). In this article, we characterize all finitely generated groups G for which the equality Aut_c(G) = Inn(G) holds.     

X-Inner Automorphisms,Automorphisms, and Isomorphisms of Skew Polynomial Rings

Abstract

In this paper, we examine the X-inner automorphisms, automorphisms, and isomorphisms of skew polynomial rings of the form K[x][y;δ], where K is a field of characteristic 0 and δ is a derivation of K [x] such that x ^δ is a polynomial of degree ≥ 1. We 1.  determine the group of X-inner automorphisms of K [x][ y;δ],

2.  analyze the structure of the group of automorphisms of K [x][ y;δ], and

3.  examine the isomorphism classes of skew polynomial rings of the form K [x][ y;δ].

We also provide several examples which indicate the importance of the base field in computing the X-inner automorphisms, automorphisms, and isomorphism classes of K [x][ y;δ].     

Automorphisms of the algebra ofq-difference operators

In this paper, automorphisms of the algebra ofq-difference operators, as an associative algebra for arbitraryq and as a Lie algebra forq being not a root of unity, are determined. Project supported by the NNSF of China     

Shift Automorphisms of the Hyperfinite Factor

For a large class of shift transformations of a LEBESGUE measure space (they have to fulfil some mixing condition) we construct automorphisms of the hyperfinite factor of type II₁. The CONNES -STØRMER entropy of the resulting automorphisms equals the measure theoretic entropy of the corresponding shift transformations. Two such automorphisms are conjugate if the conjugacy between the original measure space shifts can be given by a code with finite expected code length.     

Noetherian Automorphisms of Groups

An automorphism α of a group G is called a noetherian automorphism if for each ascending chain

Automorphisms of Cayley graphs

The aim of this paper is to characterize subgroups of non-regular automorphism groups of Cayley graphs. Relations between group automorphisms, graph automorphisms and permutations of the edge set of Cayley graphs are investigated.     

Automorphisms of metacyclic groups

A metacyclic group H can be presented as 〈α,β: αⁿ = 1, β^m = α^t, βαβ^?1 = α^r〉 for some n, m, t, r. Each endomorphism σ of H is determined by \(\sigma(\alpha)=\alpha^{x_1}\beta^{y_1}, \sigma(\beta)=\alpha^{x_2}\beta^{y_2}\) for some integers x₁, x₂, y₁, y₂. We give sufficient and necessary conditions on x₁, x₂, y₁, y₂ for σ to be an automorphism.     

Automorphisms of hyperelliptic GAG-codes

We determine the n-automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.     

Automorphisms of lexicographic products

The automorphism group Γ(P) of a partially ordered set P consists of all permutations on P that preserve order (and have order preserving inverses). In this paper we raise, and partially answer, the question: How is the automorphism group of the lexicographic product (P × Q) of two orders (P and Q) related to the automorphism groups of the factors, P and Q?We show that the wreath product Γ(Q) wr ΓP) is always contained in Γ(P × Q). We find necessary and sufficient conditions for Γ(P × Q) to equal Γ(Q) wr Γ(P), and when P and Q are finite, we find a complete characterization of Γ(P × Q) in terms of Γ(P), Γ(Q) and properties of P and Q.     

Automorphisms of imbedded graphs

If a linear graph is imbedded in a surface to form a map, then the map has a group of automorphisms which is a subgroup (usually, a proper subgroup) of the automorphism group of the graph. In this note it will be shown that, for any imbedding of K_n in an orientable surface, the order of the automorphism group of the resulting map is a divisor of n(n − 1), and that the order equals n(n − 1) if and only if n is a prime power. The explicit construction of imbeddings of K_Q, q = p^m with map automorphism group of order q(q − 1) gives rise to new types of regular map. There are also tenous connections with the theory of Frobenius groups.