We prove that any two continuous minimal (topologically free) actions of the infinite dihedral group on an compact Hausdorff space are continuously orbit equivalent only if they conjugate. also show above fails we replace by certain other virtually cyclic groups, e.g., direct product integer with non-abelian finite simple group.

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell–Jones conjecture can be reduced to only those virtually cyclic groups that admit a surjection with finite kernel onto a cyclic group. The second is that the Waldhausen Nil gro...

a k-nacci sequence in a finite group is a sequence of group elements x0 , x1, x2 ,, xn , forwhich, given an initial (seed) set 0 1 2 1 , , , ,j x x x x  , each element is defined by0 1 11 1for ,for .nnn k n k nxx x j n kxx x x n k        in this paper, we examine the periods of the k-nacci sequences in miller’s generalization of the polyhedralgroups 2,2 2;q , n,2 2;q , 2, n 2;...

a recursive-circulant $g(n; d)$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$g(n; d)$ is vertex-transitive, and has some strong hamiltonianproperties. $g(n; d)$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. in this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. in particular, wewill find that the autom...

In the title compound, C(19)H(18)N(3) (+)·Br(-)·H(2)O, the dihedral angle between the allyl group and the imidazole ring is 89.59 (14)°, while the dihedral angle between the cyanophenyl ring and the imidazole ring is 78.72 (7)°. O-H⋯Br hydrogen bonds form an infinite chain in the c-axis direction and C-H⋯Br and C-H⋯O inter-actions expand this chain into an infinite three-dimensional network.

this paper, deals with some equivalence relations in fuzzy subgroups. further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

For a given element $g$ of finite group $G$, the probablility that commutator randomly choosen pair elements in $G$ equals is relative commutativity degree $g$. In this paper we are interested studying Dihedral order $2n$ and Quaternion $2^{n}$ for any $n\geq 3$ examine infinite class Moufang Loops Chein type, $M(G,2)$.

We construct a new infinite family of four-dimensional isolated symplectic singularities with trivial local fundamental group, answering question Beauville raised in 2000. Three constructions are presented for this family: (1) as blowups the quotient C 4 $\mathbb {C}^4$ by dihedral group order 2 d $2d$ , (2) singular points Calogero–Moser spaces associated groups at equal parameters, and (3) ce...

We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lück-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In particular, we study how to obtain the Mahler measure over an infinite group as limit of Mahler measures over finite groups, for example, in the classical case of the f...

This paper investigates a connection between self-similar group representations and induced rational maps on the projective space which preserve spectrum of group. The focus is infinite dihedral D?. main theorem states that Julia set map F P2 for D? union with F's extended indeterminacy set. Moreover, limit function iteration sequence {F?n} Fatou fully described. discovery finds an application ...