For any connected complex reductive group G, finitely generated discrete ? and a normal subgroup ?˜ with quotient ?, we study the associated G??-character variety, space of admissible G??-representations ?. We relation between this variety ?-fixed points in usual G-character to ?˜. In process, give classification isomorphism classes semi-direct products G??, fixed G ?. case where are fundamenta...

Let G be a connected reductive linear algebraic group defined over an field k of characteristic not 2, θ ∈ Aut(G) an involutional k-automorphism of G and K = Gθ = {g ∈ G | θ(g) = g} the set of fixed points of θ. Denote the set of k-rational points of G by Gk. In this paper we shall classify the K-conjugacy classes of θ-stable maximal tori of G. This is shown to be independent of the characteris...

In this paper we construct a new interactive identification scheme based on the conjugacy problem. We prove that this scheme is secure against passive attacks if the matching triple search problem (MTSP) is intractable. Our proof is based on the fact that the conjugacy search problem (CSP) is hard in braid group, on the other hand, the conjugacy decision problem (CDP) is easy in braid group by ...

We discuss the complexity of conjugacy problem in Miller’s groups. We stratify the groups in question and show that for “almost all”, in some explicit sense, elements, the conjugacy search problem is decidable in cubic time. It is worth noting that a Miller’a group may have undecidable conjugacy search problem; our results show that “hard” instances of the problem comprise a negligibly small pa...

It is proved that for any prime p a finitely generated nilpotent group is conjugacy separable in the class of finite p-groups if and only if the tor-sion subgroup of it is a finite p-group and the quotient group by the torsion subgroup is abelian. 1. Let K be a class of groups. A group G is called residual K (or K-residual) if for each non-unit element a ∈ G there is a homomorphism ϕ of G onto ...

In this paper, we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution cone convexity, is straightforward. The results are established under verifiable Slater-type condition, with relaxed monotonicity without lower semicontinuity assumptions the play. versatility of our findings illust...

we present the basic results on the representation theory of the alternating groups. our approach is based on clifford theory.

We establish new conjugacy criteria for half-linear second order differential equations. These criteria are based on the relationship between conjugacy of the investigated equation and nonpositivity of the associated energy functional.