Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New necessary conditions for Payley type PDS in Abelian groups   In this paper we prove that if there is a regular Paley type partial
difference set in an Abelian group $G$ of order $v$, where
$v=p_1^{2k_1}p_2^{2k_2}\cdots p_n^{2k_n}$, $n\ge 2$, $p_1$, $p_2$, $\cdots$,
$p_n$ are distinct odd prime numbers, then for any $1 \le i \le n$, $p_i$ is
congruent to 3 modulo 4 whenever $k_i$ is odd. These new necessary conditions
further limit the specific order of an Abelian group $G$ in which there can
exist a Paley type partial difference set. Our result is similar to a result on
Abelian Hadamard (Menon) difference sets proved by Ray-Chaudhuri and Xiang in
1997.

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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th