Search results for "Dihedral group"
showing 6 items of 6 documents
Products of locally dihedral subgroups
2012
AbstractIt is shown that a group G=AB which is a product of two periodic locally dihedral subgroups A and B is soluble.
On permutations of class sums of alternating groups
1997
We prove a result concerning the class sums of the alternating group An; as a consequence we deduce that if θ is a normalized automorphism of the integral group ring then there exists such that is the identity on , where Sn:is the symmetric group and is the center of
Enumerating the Walecki-Type Hamiltonian Cycle Systems
2017
Let Kv be the complete graph on v vertices. A Hamiltonian cycle system of odd order v (briefly HCS(v)) is a set of Hamiltonian cycles of Kv whose edges partition the edge set of Kv. By means of a slight modification of the famous HCS(4n+1) of Walecki, we obtain 2n pairwise distinct HCS(4n+1) and we enumerate them up to isomorphism proving that this is equivalent to count the number of binary bracelets of length n, i.e. the orbits of Dn, the dihedral group of order 2n, acting on binary n-tuples.
Local nearrings with dihedral multiplicative group
2004
AbstractA not necessarily zero-symmetric nearring R with a unit element is called local if the set of all non-invertible elements of R forms a subgroup of the additive group of R. It is proved that every local nearring whose multiplicative group is dihedral is finite and its additive group is either a 3-group of order at most 9 or a 2-group of order at most 32.
Stability of dark matter from the D4×Z2f flavor group
2011
Abstract We study a model based on the dihedral group D 4 in which the dark matter is stabilized by the interplay between a remnant Z 2 symmetry, of the same spontaneously broken non-abelian group, and an auxiliary Z 2 f introduced to eliminate unwanted couplings in the scalar potential. In the lepton sector the model is compatible with normal hierarchy only and predicts a vanishing reactor mixing angle, θ 13 = 0 . Since m ν 1 = 0 , we also have a simple prediction for the effective mass in terms of the solar angle: | m β β | = | m ν 2 | sin 2 θ ⊙ ∼ 10 − 3 eV . There also exists a large portion of the model parameter space where the upper bounds on lepton flavor violating processes are not …
MR 2776821 Reviewed Berger E. Hurwitz equivalence in dihedral groups. The Electronic Journal of Combinatorics 18 (2011), no.1, paper 45, 16 pp. (Revi…
2011
In the paper under review, the author studies the orbits of the action of the braid group B_{n} on G^{n} where G denoted a dihedral group. At first, the author considers tuples T consisting only of reflections. In this case, the author proves that the orbits are determinate by three invariants. These invariants are the product of the entries, the subgroup generated by the entries and the number of times each conjugacy class is represented in T. Successively, the author works with tuples whose entries are any elements of dihedral groups. The author shows that, also this time, the above invariants are sufficient in order to determinate the orbits of the action of B_{n} on G^{n}.