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- W3147823757 abstract "A McFarland difference set is a difference set with parameters (v,k, 2 )= (qd+l(qd+qa-l+...+q+2),qa(qd+qa l + . . . + q + l ) , qd(qa-l+qa-2+...+ q + 1)), where q=p/and p is a prime. Examples for such difference sets can be obtained in all groups of G which contain a subgroup E ~-EA(q a+ 1) such that the hyperplanes of E are normal subgroups of G. In this paper we study the structure of the Sylow p-subgroup P of an abelian group G admitting a McFarland difference set. We prove that if P is odd and P is self-conjugate modulo exp(G), then p ~_ EA(qa+ 1). For p = 2, we have some strong restrictions on the exponent and the rank of P. In particular, we show that iff>~2 and 2 is self-conjugate modulo exp(G), then exp(P)~<max{2 f i , 4}. The possibility of applying our method to other difference sets has also been investigated. For example, a similar method is used to study abelian (320, 88, 24)-difference sets. © 1995 Academic Press, Inc." @default.
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- W3147823757 date "2004-01-01" @default.
- W3147823757 modified "2023-09-23" @default.
- W3147823757 title "The Structure of the Abelian Groups Containing McFarland Difference Sets" @default.
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- W3147823757 hasPublicationYear "2004" @default.
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