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A Note on Certain 2-Groups with Hadamard Difference Sets

✍ Scribed by J. E. Iiams


Book ID
110299218
Publisher
Springer
Year
2001
Tongue
English
Weight
42 KB
Volume
23
Category
Article
ISSN
0925-1022

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Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Hadamard difference sets. In the abelian case, a group of order 2 2 tq2 has a difference set if and only if the exponent of the group is less tq 2 Ε½ than or equal to 2 . In a previous work R.

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## Abstract Let __M__ be an arbitrary structure. Then we say that an __M__ ‐formula __Ο†__ (__x__) __defines a stable set in__ __M__ if every formula __Ο†__ (__x__) ∧ __Ξ±__ (__x__, __y__) is stable. We prove: If __G__ is an __M__ ‐definable group and every definable stable subset of __G__ has __U__ ‐