We show that the homotopy type of a finite oriented Poincar\'{e} 4-complex is determined by its quadratic 2-type provided fundamental group and has dihedral Sylow 2-subgroup. By combining with results Hambleton-Kreck Bauer, this applies in case smooth 4-manifolds whose subgroup SO(3). An important class examples are elliptic surfaces group.

Every virtually cyclic group Γ that surjects onto the infinite dihedral group D∞ contains an index two subgroup Π of the form H ⋊α Z. We show that the Waldhausen Nil-group of Γ vanishes if and only if the Farrell Nil-group of Π vanishes. 1. Statement of results. The Bass Nil-groups, Farrell Nil-groups, and Waldhausen Nil-groups appear respectively as pieces in the computation of the algebraicK-...

In the title compound, C(21)H(21)NO, the indene ring system is essentially planar with a maximum deviation of 0.066 (1) Å and makes dihedral angles of 7.93 (6) and 2.43 (6)°, respectively, with the benzene plane and the mean plane of the piperidine ring. These latter two planes make a dihedral angle of 7.61 (7)°. In the crystal, mol-ecules are linked by C-H⋯O inter-actions, forming infinite cha...

s Prof. Paul Baginski Title: Definability and Nilpotence in Groups with Bounded Chains of Centralizers Abstract: A group G has bounded chains of centralizers (G is MC) if every chain of centralizers CG(A1) ≤ CG(A2) ≤ . . . is finite. While this class of groups is interesting in its own right, within the field of logic known as model theory, MC groups have been examined because they strictly con...

A graph is one-regular if its automorphism group acts regularly on the arc set. In this paper, we construct a new infinite family of one-regular Cayley graphs of any prescribed valency. In fact, for any two positive integers , k 2 except for ( , k) ∈ {(2,3), (2,4)}, the Cayley graph Cay(Dn,S) on dihedral groups Dn = 〈a, b | an = b2 = (ab)2 = 1〉 with S = {a1+ +···+ t b | 0 t k − 1} and n = ∑k−1 ...