Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost Difference Sets in Nonabelian Groups   We give two new constructions of almost difference sets. The first is a
generic construction of $(q^{2}(q+1),q(q^{2}-1),q(q^{2}-q-1),q^{2}-1)$ almost
difference sets in certain groups of order $q^{2}(q+1)$ ($q$ is an odd prime
power) having ($\mathbb{F}_{q},+)$ as a subgroup. The construction occurs in
any group of order $p^{2}(p+1)$ ($p$ is an odd prime) having
($\mathbb{F}_{p^{2}},+)$ as an additive subgroup. This construction yields
several infinite families of almost difference sets, many of which occur in
nonabelian groups. The second construction yields $(4p,2p+1,p,p-1)$ almost
difference sets in dihedral groups of order $4p$ where $p\equiv 3 \ ({\rm mod}
\ 4)$ is a prime. Moreover, it turns out that some of the infinite families of
almost difference sets obtained have Cayley graphs which are Ramanujan graphs.
\keywords{Difference set \and Almost difference set \and Nonabelian group}

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph