On Sylow Subgroups of Abelian Affine Difference Sets
An n-subsetD of a group G of order n2−1 is called an affine difference set of G relative to a normal subgroup N of G of order n−1 if the list of differences d1d2-1 (d1, d2 ∈ D, d1 ≠ d2) contain search element of G-N exactly once and no element of N. It is a well-known conjecture that if D is an aff...
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| 格式: | text |
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Archīum Ateneo
2001
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| 在線閱讀: | https://archium.ateneo.edu/mathematics-faculty-pubs/91 https://link.springer.com/article/10.1023%2FA%3A1008312921730 |
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| 機構: | Ateneo De Manila University |
| 總結: | An n-subsetD of a group G of order n2−1 is called an affine difference set of G relative to a normal subgroup N of G of order n−1 if the list of differences d1d2-1 (d1, d2 ∈ D, d1 ≠ d2) contain search element of G-N exactly once and no element of N. It is a well-known conjecture that if D is an affine difference set in an abelian group G, then for every prime p, the Sylow p-subgroup of G is cyclic. In Arasu and Pott [1], it was shown that the above conjecture is true when p = 2. In this paper we give some conditions under which the Sylow p-subgroup of G is cyclic. |
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