The cyclic group of order nine is the smallest group for which the number of orthomorphisms has not been determined theoretically. In [2], using the “method.
Oct 5, 2010 � An orthomorphism of the cyclic group Zn is a permutation σ:Zn→Zn such that i↦σ(i)−i is also a permutation.
Missing: nine. | Show results with:nine.
By giving previously unknown a pair of orthogonal orthomorphisms of cyclic groups of order 18 t + 9 for any positive integer t, we complete the existence�...
Missing: nine. | Show results with:nine.
People also ask
Are groups of order 9 Abelian?
How do you find the cyclic group of a number?
Namely, we show that no multiplicative orthomorphisms exist for n > 2, but that exponential orthomorphisms exist whenever n is twice a prime p such that p − 1�...
Missing: nine. | Show results with:nine.
Apr 20, 2011 � There are, up to isomorphism, two possibilities for a group of order 9. Both of these are abelian groups and, in particular are abelian of prime power order.
Missing: orthomorphisms | Show results with:orthomorphisms
We develop the theory of compound, compatible and polynomial orthomorphisms and the relationships between these classes.
Missing: nine. | Show results with:nine.
In the process we will show how the orthogonal pair of orthomorphisms, constructed in [9], can be obtained by solving the difference equations (2) and adjacency�...
We prove that if m � 3 is odd and not divisible by 9 then we can construct a pair of orthogonal orthomorphisms of Zm. From this we derive new lower bounds�...
Missing: nine. | Show results with:nine.
We say κ is canonical if κ(0)=0 and define zn to be the number of canonical orthomorphisms of Zn. If n=dt and κ(i)≡κ(j)(modd) whenever i≡j(modd) then κ is�...
Missing: nine. | Show results with:nine.
For instance, in the case n = 9 it is rapidly established that there are exactly 21 sets of. 8 mutually orthogonal latin squares obtained from the elementary�...