A class of non-abelian 2-groups containing Menon difference sets

We show that every group in a certain class of 2-groups contains a Menon difference set. This provides further positive evidence for a conjecture of Dillon concerning 2-groups of order 2 2 l which contain a normal subgroup isomorphic to Z l 2. The conjecture, however, remains open.

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 62; no. 1; pp. 57 - 62
Main Authors Meisner, D.B., Piper, F.C., Wild, P.R.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 21.07.1997
Subjects
2-group
Difference set
Hadamard
Menon
Non-abelian
Relative difference set
05B10
Non-abelian
Hadamard
2-group
Menon
Difference set
62K10
Relative difference set
051320
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Summary:We show that every group in a certain class of 2-groups contains a Menon difference set. This provides further positive evidence for a conjecture of Dillon concerning 2-groups of order 2 2 l which contain a normal subgroup isomorphic to Z l 2. The conjecture, however, remains open.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(96)00168-1