In the present paper, we study outer automorphism groups of absolute Galois mixed-characteristic local fields from point view anabelian geometry. Let us recall that it is well-known natural homomorphism group a field to given injective. One main result paper if satisfies certain conditions, then set conjugates image this injective in infinite, which thus implies not normal group. particular, on...

In this paper we use orderly algorithms to enumerate (perfect) one-factorizations of complete graphs, the automorphism groups of which contain certain prescribed subgroups. We showed that, for the complete graph Ki2, excluding those one-factorizations containing exactly one automorphism of six disjoint cycles of length two, there are precisely 56391 nonisomorphic one-factorizations of Ki2 with ...

The present paper deals with permutations induced by tame automorphisms over finite fields. The first main result is a formula for determining the sign of the permutation induced by a given elementary automorphism over a finite field. The second main result is a formula for determining the sign of the permutation induced by a given affine automorphism over a finite field. We also give a combini...

In this paper we investigate when the generic member of a family of complex K3 surfaces admitting a non–symplectic automorphism of finite order admits also a symplectic automorphism of the same order. We give a complete answer to this question if the order of the automorphism is a prime number and we provide several examples and partial results otherwise. Moreover we prove that, under certain c...

Let G be a group. The orbits of the natural action \({{\,\mathrm{Aut}\,}}(G)\) on are called automorphism G, and number is denoted by \(\omega (G)\). virtually nilpotent group such that (G)< \infty \). We prove \(G = K \rtimes H\) where H torsion subgroup torsion-free radicable characteristic G. Moreover, we \(G^{'}= D \times {{\,\mathrm{Tor}\,}}(G^{'})\) subgroup. In particular, if maximum nor...

In this paper we shall present a natural generalisation of the notion of automorphism of a graph or digraph G, namely a two-fold automorphism. This is a pair (α, β) of permutations of the vertex set V(G) which acts on ordered pairs of vertices of G in the natural way. The action of (α, β) on all such ordered pairs gives a graph which is two-fold isomorphic to G. When α = β the two-fold automorp...

A regular Cayley map for a finite group A is an orientable map whose orientation-preserving automorphism group G acts regularly on the directed edge set and has a subgroup isomorphic to A that acts regularly on the vertex set. This paper considers the problem of determining which abelian groups have regular Cayley maps. The analysis is purely algebraic, involving the structure of the canonical ...

Scmicomplctc nilpotcnt groups, that is, nilpotent groups with no outer automorphisms, have been of interest for many years. In this paper pscudocomplete nilpotent groups, that is, nilpotent groups in which the automorphism group and the inner automorphism group arc isomorphic (not equal), are constructed. When suitable conditions are placed on the pseudocomplete nilpotent group, the quotient of...

If p is prime, a compact Riemann surface X of genus g ≥ 2 is called cyclic p-gonal if it admits a cyclic group of automorphisms Cp of order p such that the quotient space X/Cp has genus 0. If in addition Cp is not normal in the full automorphism A, then we call X a non-normal p-gonal surface. In the following we classify all non-normal p-gonal surfaces. A. Wootton University of Portland 5000 No...