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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Archīum Ateneo
2001
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ph-ateneo-arc.mathematics-faculty-pubs-10902020-06-18T07:53:56Z On Sylow Subgroups of Abelian Affine Difference Sets Garciano, Agnes Hiramine, Yutaka 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. 2001-01-01T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/91 https://link.springer.com/article/10.1023%2FA%3A1008312921730 Mathematics Faculty Publications Archīum Ateneo affine difference sets projective planes collineation groups Mathematics |
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affine difference sets projective planes collineation groups Mathematics |
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affine difference sets projective planes collineation groups Mathematics Garciano, Agnes Hiramine, Yutaka On Sylow Subgroups of Abelian Affine Difference Sets |
| description |
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. |
| format |
text |
| author |
Garciano, Agnes Hiramine, Yutaka |
| author_facet |
Garciano, Agnes Hiramine, Yutaka |
| author_sort |
Garciano, Agnes |
| title |
On Sylow Subgroups of Abelian Affine Difference Sets |
| title_short |
On Sylow Subgroups of Abelian Affine Difference Sets |
| title_full |
On Sylow Subgroups of Abelian Affine Difference Sets |
| title_fullStr |
On Sylow Subgroups of Abelian Affine Difference Sets |
| title_full_unstemmed |
On Sylow Subgroups of Abelian Affine Difference Sets |
| title_sort |
on sylow subgroups of abelian affine difference sets |
| publisher |
Archīum Ateneo |
| publishDate |
2001 |
| url |
https://archium.ateneo.edu/mathematics-faculty-pubs/91 https://link.springer.com/article/10.1023%2FA%3A1008312921730 |
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1681506678848094208 |