Frey and Kani put a particular modular space structure on the space of a space of modular curves that resembles a Hurwitz space structure. We follow up on this, simplifying the group theory so that properties of this space are clear. For the rst, Prop. 2.4 shows it is simple to characterize the monodromy group of Frey-Kani covers of degree N (and that it is S N). In anticipation of other proble...

Suppose that G is a …nite solvable group which has an irreducible character which vanishes on exactly one conjugacy class. Then we show that G has a homomorphic image which is a nontrivial 2-transitive permutation group. The latter groups have been classi…ed by Huppert. We can also say more about the structure of G depending on whether is primitive or not. Mathematics Subject Classi…cation 2000...

Let G be an adjoint simple algebraic group over an algebraically closed field of characteristic p; let be the root system of G, and take t ∈ N. Lawther has proven that the dimension of the set G[t] = {g ∈G : g = 1} depends only on and t . In particular the value is independent of the characteristic p; this was observed for t small and prime by Liebeck. Since G[t] is clearly a disjoint union of ...

We prove the conjugacy separability of groups of the form G = (ax,...ar,bx,...,bs:aeli = bf> = (U(ax, ... , ar)V{bx , ... , bs))m = 1), where m > 1 .

Let Mn be the vector space of all n × n-matrices over an algebraically closed field F of characteristic zero. We describe the linear span of the conjugacy class (with respect to the full linear group GLn) of an arbitrary matrix A ∈ Mn, and derive the existence of some particular bases of Mn. Moreover, we propose certain observations on finite sequences of nilpotent matrices and their linear spa...

Abstract Let $$\pi $$ ? be a set of primes. We show that -separable groups have conjugacy class $${\mathfrak {F}}$$ F -injectors for suitable Fitting classes , which coincide with the usual ones when specializing to soluble groups.

Let G be a finite group and let K = x the conjugacy class of an element G. In this paper, it is proved that if N normal subgroup such coset union ? 1 (the inverse x), then ? ? are solvable. As application, we prove there exists natural number n ? 2 ? ,

In this paper we introduce the geodesic conjugacy language and geodesic conjugacy growth series for a finitely generated group. We study the effects of various group constructions on rationality of both the geodesic conjugacy growth series and spherical conjugacy growth series, as well as on regularity of the geodesic conjugacy language and spherical conjugacy language. In particular, we show t...

Let X be a locally compact Hausdorff space with n proper continuous self maps σi : X → X for 1 ≤ i ≤ n. To this we associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra A(X, τ) and the semicrossed product C0(X)×τ Fn . We develop the necessary dilation theory for both models. In particular, we exhibit an expli...