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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Main Authors: Garciano, Agnes, Hiramine, Yutaka
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Published: Archīum Ateneo 2001
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Online Access:https://archium.ateneo.edu/mathematics-faculty-pubs/91
https://link.springer.com/article/10.1023%2FA%3A1008312921730
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Institution: Ateneo De Manila University
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spelling 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
institution Ateneo De Manila University
building Ateneo De Manila University Library
country Philippines
collection archium.Ateneo Institutional Repository
topic affine difference sets
projective planes
collineation groups
Mathematics
spellingShingle 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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