Sequencing certain dihedral groups
β Scribed by John Isbell
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 411 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
At least three-fourths of the dihedral groups D, are sequenceable: all but D3 and D4 (which are not sequenceable) and perhaps Dbk for k 3 13. Sequencings are related to especially effective shuffles of a deck of cards.
π SIMILAR VOLUMES
## Abstract Let __L/F__ be a dihedral extension of degree 2__p__, where __p__ is an odd prime. Let __K/F__ and __k/F__ be subextensions of __L/F__ with degrees __p__ and 2, respectively. Then we will study relations between the __p__βranks of the class groups Cl(__K__) and Cl(__k__). (Β© 2005 WILEYβ
We give a specific construction of 2-sequencings in the dihedral groups O4k. A finite group G is called sequenceable, if its elements can be listed: a2,a3 ..... an,
## Abstract If __n__ is divisible by at least three distinct primes, the dihedral group __D~n~__ can be generated by three nonredundant, involuntary elements. We study the Cayley graphs resulting from such a presentation of __D~n~__ for several families of __n__ and for all admissible __n__ < 120.
We prove that for any primes p 1 ; . . . ; p s there are only finitely many numbers Q s iΒΌ1 p ai i ; a i 2 Z ΓΎ ; which can be orders of dihedral difference sets. We show that, with the possible exception of n ΒΌ 540; 225; there is no difference set of order n with 15n410 6 in any dihedral group.